SHM - Simple Harmonic Motion - Physics A-level Required Practical

Summary

In this MSB science video, Mr. Reese demonstrates the practical steps for conducting A-level physics experiments on simple harmonic motion using a simple pendulum and a mass-spring system. He explains how to measure the time period of oscillations by changing the length of the pendulum string and the mass on the spring, ensuring accuracy with a ruler and a fiducial marker. The video guides viewers through the process of collecting data, calculating the time period for different lengths and masses, and plotting graphs to verify the relationship between time period and the physical properties of the systems.

Takeaways

• 🔍 Mr. Reese from MSB Science is demonstrating A-Level physics experiments on simple harmonic motion.
• 📏 For the pendulum experiment, the length of the string is varied to measure the period of oscillations.
• 📐 A high-resolution ruler is used to ensure accurate measurements, with measurements taken from the bottom of the wood to the center of the pendulum bob.
• 🔩 The string is clamped between pieces of wood to ensure the pivot point is fixed at the bottom.
• 🧷 A nail is used as a fiducial marker to track the pendulum's motion without touching it.
• 🔄 The pendulum is displaced about 10° to ensure accuracy, as larger amplitudes reduce the accuracy of the experiment.
• ⏱️ Time is measured for 10 oscillations and then averaged to find the period of one oscillation.
• 📉 The relationship between the square of the period (T^2) and the length of the string is graphed to find the gradient, which is proportional to the acceleration due to gravity (g).
• 🔗 The mass-spring system experiment is similar to the pendulum, using a spring and a clamp to create oscillation.
• 📊 The graph of T^2 against mass (m) should be a straight line, indicating that T^2 is proportional to m, allowing for the calculation of the spring constant (K).
• 🔍 The Hooke's Law experiment can be conducted to find the spring constant (K) and verify the results obtained from the mass-spring system.

Q & A

What is the purpose of the practical demonstrated in the script?

The purpose of the practical is to study simple harmonic motion using a simple pendulum and a mass-spring system, by measuring the time period of oscillations for different lengths of the pendulum string and different masses on the spring.

Why is it important to ensure the pivot is at the bottom of the pieces of wood when setting up the pendulum?

Ensuring the pivot is at the bottom of the pieces of wood is important to guarantee that the pivot is fixed at the bottom, which is necessary for accurate measurements of the pendulum's length.

What is the significance of using a ruler with 1 mm resolution in this experiment?

A ruler with 1 mm resolution is used for more accurate measurements of the pendulum's length, which is crucial for the precision of the experiment.

Why is it necessary to measure from the bottom of the wood to the middle of the bob?

Measuring from the bottom of the wood to the middle of the bob ensures that the measurement is taken to the center of mass, not to the top or bottom of the bob, which would introduce errors.

What is the role of the nail as a fiducial marker in the experiment?

The nail serves as a fiducial marker to provide a reference point for the pendulum's position, allowing for accurate timing of the oscillations.

Why is it advised not to displace the pendulum too far from equilibrium?

Displacing the pendulum too far from equilibrium can lead to a larger amplitude, which makes the equation used for calculating the time period less accurate.

How does measuring the time for 10 oscillations instead of one improve accuracy?

Measuring the time for 10 oscillations and then averaging it reduces random errors and provides a more accurate estimate of the time period for one oscillation.

What is the equation relating the time period (T) to the length (L) of the pendulum string?

The equation relating the time period (T) to the length (L) of the pendulum string is T = 2π√(L/g), where g is the acceleration due to gravity.

Why is it necessary to square the time period when plotting the graph for the pendulum?

Squaring the time period allows for a linear relationship between T^2 and L, which is easier to analyze and graph, as T^2 is proportional to L.

How does changing the mass on the spring affect the time period of oscillation?

The time period of oscillation for a mass-spring system is given by T = 2π√(m/k), where m is the mass and k is the spring constant. Changing the mass will affect the time period according to this relationship.

What is the significance of plotting T^2 against M for the mass-spring system?

Plotting T^2 against M for the mass-spring system allows for the determination of the spring constant (k) by analyzing the gradient of the resulting straight line graph.

Outlines

00:00

🔍 Demonstrating Simple Harmonic Motion with a Pendulum

In this segment, Mr. Reese from MSB Science demonstrates an A-level physics experiment on simple harmonic motion using a simple pendulum. The objective is to measure the time period of pendulum oscillations for different lengths of the string. To ensure accuracy, a wooden clamp is used to secure the string at a fixed pivot point. A ruler with 1 mm resolution is used to measure the length from the bottom of the clamp to the center of the pendulum bob. The experiment involves varying the string length from 10 cm to 100 cm and measuring the time for 10 oscillations, then averaging this time to find the period of one oscillation. A fiducial marker is used to accurately track the pendulum's position. The goal is to verify the equation T = 2π√(L/g), where T is the time period, L is the length of the string, and g is the acceleration due to gravity. The results are plotted as T² against L to find the gradient, which is then used to calculate g.

05:03

📏 Investigating Simple Harmonic Motion with a Mass-Spring System

In the second paragraph, Mr. Reese continues the discussion on simple harmonic motion but now with a mass-spring system. The experiment involves attaching a mass to a spring and observing its oscillation. A fiducial marker is placed close to the mass to track its motion. The mass is initially set to 100 grams and then increased to 500 grams. The time period for one oscillation is measured for each mass, and the results are used to plot T² against mass (M). The equation T = 2π√(m/K) is used, where m is the mass and K is the spring constant. By plotting T² against M, a straight line is expected, indicating that T² is proportional to M. The gradient of this line is used to calculate the spring constant (K), which can be verified by comparing it with the value obtained from Hooke's Law experiment.

Keywords

💡Simple Harmonic Motion

Simple Harmonic Motion (SHM) is a type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. In the context of the video, SHM is demonstrated through a simple pendulum and a mass-spring system. The video aims to show how to measure the time period of these systems' oscillations, which is a key aspect of understanding SHM.

💡Pendulum

A pendulum is a weight suspended from a fixed point so that it can swing freely back and forth under the influence of gravity. The script describes an experiment with a simple pendulum where the length of the string is varied to observe its effect on the period of oscillation. This is crucial for understanding the principles of SHM as the period of a simple pendulum is related to its length.

💡Time Period

The time period of an oscillating system is the time taken for one complete cycle of the motion. In the video, the time period is measured for the pendulum and mass-spring system over multiple oscillations to ensure accuracy. The script emphasizes the importance of measuring the time for 10 oscillations and then averaging it to find the period of one oscillation.

💡Fiducial Marker

A fiducial marker is a reference point used in the experiment to accurately measure the position of the oscillating object. In the script, a nail is used as a fiducial marker to track the pendulum's position. It is placed close to the string but not touching it, ensuring that the measurements are precise and that the marker does not interfere with the pendulum's motion.

💡Amplitude

Amplitude refers to the maximum displacement of the oscillating object from its equilibrium position. The script mentions displacing the pendulum about 10° from equilibrium, which is a small amplitude. It is important to keep the amplitude small to ensure that the motion remains simple harmonic and the equations used for analysis are valid.

💡Spring Constant

The spring constant (K) is a measure of the stiffness of a spring, defined as the force needed to extend or compress the spring by one unit of length. In the video, the spring constant is an important parameter in the equation relating the time period of a mass-spring system to the mass attached to it. The script describes an experiment where the mass is varied to find the relationship between the time period and the spring constant.

💡Equilibrium

Equilibrium in physics refers to a state where all forces acting on a system are balanced, resulting in no net force and no acceleration. In the script, the pendulum is said to be at equilibrium when it is in its rest position, and the fiducial marker is aligned with this position. The experiment starts timing when the pendulum passes this equilibrium point.

💡Displacement

Displacement is the change in position of an object. In the context of SHM, it refers to how far the oscillating object is from its equilibrium position. The script describes displacing the pendulum and the mass-spring system from their equilibrium positions to initiate the oscillation.

💡Mass-Spring System

A mass-spring system is a simple model used to study SHM, consisting of a mass attached to a spring. The script describes an experiment where the mass is varied by adding different weights to the spring to observe how the time period changes. This system is used to demonstrate the principles of SHM and to derive the relationship between the time period, mass, and spring constant.

💡Hooke's Law

Hooke's Law states that the force (F) needed to extend or compress a spring by some distance (x) is proportional to that distance, or F = -kx, where k is the spring constant. The script mentions Hooke's Law in the context of verifying the spring constant (K) by plotting a graph of force against extension, which should yield a straight line if the law holds true.

💡Graph

A graph is a visual representation of data, often used to display relationships between variables. In the script, the instructor plans to plot graphs of the square of the time period (t^2) against the length of the pendulum string (L) and the mass (M) to verify the equations for SHM. These graphs help visualize the proportional relationships and can be used to calculate constants like G (acceleration due to gravity) and K (spring constant).

Highlights

Introduction to A Level Physics practical on simple harmonic motion.

Demonstration of simple pendulum experiment setup.

Explanation of clamping the string to ensure pivot is at the bottom.

Use of a ruler with 1 mm resolution for accurate measurements.

Measurement from the bottom of the wood to the middle of the bob.

Choice of string length range from 10 cm to 100 cm.

Use of a light and inextensible thread for the pendulum.

Employment of a nail as a fiducial marker for precision.

Procedure for displacing the pendulum about 10° for oscillation.

Emphasis on measuring time for 10 oscillations for accuracy.

Calculation of the time period for one oscillation.

Explanation of the equation T = 2π√(L/g).

Graphing T^2 against L to find the gradient.

Verification of the relationship by finding G.

Introduction to the mass-spring system experiment.

Procedure for setting up the mass-spring system.

Explanation of the relationship between time period and mass.

Graphing T^2 against mass to obtain a straight line.

Verification of spring constant K using Hooke's Law.

Transcripts

hi it's Mr Reese here from MSB science

and I'm going to show you how to do the

a level physics required practical or

practicals on simple harmonic motion for

a simple pendulum and a mass spring

system with the pendulum what we want to

do is change the length of the string

and then we're going to measure the time

period of its oscillations now I've used

a couple of pieces of wood to clamp the

string in between because if it was just

hanging over something then that means

that the pivot would be fixed so I can

be sure that the pivot is right at the

bottom of these pieces of wood now when

we measure this we want to be fairly

accurate and so you'll need a cenm

resolution or 1 mm resolution

ruler I'm going to use a meter rule here

now I've got mine set up here for 30 cm

so I'm just going to check that that's

correct notice that I'm measuring from

the bottom of the wood to the middle of

the Bob that's to make sure that I'm

measuring to the center of mass not to

the top top of the Bob or the bottom of

the Bob you can choose what length to do

I would go from 10 cm all the way to 100

and you'll need to hang your pendulum

off the side of the table in order to do

that but that's okay now the thread that

I've used is light and it's inextensible

as well now in order to make sure that

we are being this accurate as possible

I'm going to use a nail as a fiducial

marker and I'm just going to pop that on

here and that's going to be very close

to the string although not touching it

and you don't want it too close cuz the

string will move sideways a little bit

as well and it could catch it like that

what you want to do is line up your nail

so it's directly behind the piece of

string when the pendulum is at

equilibrium then you want to get on eye

level and so if I was doing this

experiment I would have my pendulum

there and I'd be looking at eye level so

I can be sure when the string has gone

past equilibrium so I'm going to

displace the pendulum now we're going to

do it about 10° we don't want to do it

up here here the bigger our amplitude

the less accurate the equation t equal 2

piun < TK L / G is so I'm just going to

displace it this much doesn't need to be

much at all we can just set it going and

just to be clear one oscillation is now

to now it's not from one side to the

other it needs to go there back and to

the center again so I'm going to start

my stop clock when it passes equilibrium

next and obviously I would want to be at

ey level with the fiducial marker if I

was doing this for real I could measure

the time taken for one oscillation but

that's not going to be accurate so I'm

going to measure the time taken for 10

oscillations then average it don't

forget that when you start your stock

clock that's zero and then you're

counting one after that so here we go

started my stop clock now 1 2 3 4 5 6 7

8 9 10 that gives me a time of

11.56 seconds dividing that by 10 that

means that one oscillation the time

period T is going to be

1.56 seconds and then want to change the

length and do the same again so here are

my time periods for all my different

lengths I've just gone 20 cm 40 608 100

now the equation like we said is T = 2

piun L / G where L is the length of the

piece of string so we can't draw a graph

of T against L because they're not

proportional squaring the whole equation

though we can see that t^2 is

proportional to L so that's what we're

going to draw on our graph t^2 on the Y

AIS and L length of the piece of string

on the x axis finding the gradient that

is equal to according to the equation 4

pi^ 2 / G so what I can do is verify

this relationship by finding G just

swapping gradient and G over we end up

with gal 4 pi^ 2 over the gradient and

if I wanted to I could find out the

percentage error in that compared to the

accepted 9.81 m/s squared the mass

spring system is very similar all we

have to do is get a spring and what we

can do is trap

it on the arm of a clamp and we're going

to have a nail as a fiducial marker as

per usual let's start with 100 G of Mass

on the end of the spring now it's up to

you where you put your fiducial marker

but I would have it very close to the

bottom of the mass itself let's keep the

mass still so we can see where that is

there we go

and again I'd want to be at eye level

for this in reality so if I displace the

spring a little bit from equilibrium and

set to go we can see that it oscillates

nicely we don't want to pull it too far

cuz otherwise it's going to compress too

much to the top and you won't get a

proper oscillation so you really don't

need to displace it that much so again

we're going to leave it go and then

we're just going to start the stop clock

when it passes the fiducial marker and

then we're going to call that zero and

count for 10 oscillations again so

starting now 1 2 3 3 4 5 6 7 8 9 10 so

that was 3.90 seconds divided by 10

that's

0.390 seconds that's my time period for

one oscillation for 100 G then I'm going

to add more mass on and see what the

time period is again now that I've done

500 G or 0.5 kg because they do need to

be working in kilogram I'm going to plot

not t against M because similarly to the

pendulum it's not t proportional to M

the equation is T = 2 piun * < TK of m /

K where m is the mass and K is the

spring constant so Square in the whole

thing t^2 = 4 piun ^ 2 * m / K so if I

do a graph of T ^2 against M I should

end up with a straight line graph that

goes to the origin because t^2 should be

proportional to M the gradient of this

is going to be equal to 4 pi^ 2 over K

and just like last time I can swap the

gradient and K over and see what K ends

up being to verify this I can actually

carry out just the normal hooks LW

experiment to have a graph of force

against extension and that will give me

an accurate value for K and I can

compare the two