SHM - Simple Harmonic Motion - Physics A-level Required Practical
Summary
TLDRIn 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
🔍 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.
📏 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.
Mindmap
Keywords
💡Simple Harmonic Motion
💡Pendulum
💡Time Period
💡Fiducial Marker
💡Amplitude
💡Spring Constant
💡Equilibrium
💡Displacement
💡Mass-Spring System
💡Hooke's Law
💡Graph
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
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