• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month
Page
1. 1
1
2. 2
2
3. 3
3
4. 4
4
5. 5
5
6. 6
6
7. 7
7
8. 8
8
9. 9
9
10. 10
10
11. 11
11

# Physic lab report - study the simple harmonic motion (SHM) of a simple pendulum and to investigate the phase relationship between the displacement, velocity and acceleration, and to investigate how acceleration is related to displacement in a simple harmo

Extracts from this document...

Introduction

Ivan Liu Chun Pok

6A(11)

Group 8

Laboratory report: Studying a simple harmonic oscillation

Objectives:

To study the simple harmonic motion (SHM) of a simple pendulum and to investigate the phase relationship between the displacement, velocity and acceleration, and to investigate how acceleration is related to displacement in a simple harmonic motion.

Apparatus:

• half metre rule
• a light string
• pendulum bob
• video camera with tripod stand
• computer with Motion Video Analysis (MVA) software and Microsoft Excel installed

Experimental design:

Fig. 0

Theory:

For an object or mass moving in a simple harmonic motion, the displacement, velocity and acceleration change periodically in both magnitude and direction. The acceleration in particular is always proportional to its displacement from the equilibrium position and must always be directed towards the equilibrium point. Mathematically it can be expressed as
a = -kx,         where k is a constant and x is the displacement from the equilibrium point.

Also for a simple harmonic oscillation, the period or frequency of oscillation is independent of the amplitude of the motion.

In Figure 1, x is the displacement of the pendulum bob from the equilibrium point Q. Points P and R are points where the maximum displacement (amplitude A) can be obtained. Theoretically, the following equations are true for S.H.M.:
When the motion starts at the equilibrium position (point Q)

x = A sin ωt                where ω is angular velocity
v
= ω A cos ωt
a
= - ω2A sin ωt

Period T = 2 π / ω

Fig. 1

When the motion starts at the position

Middle

8.15E-03

-2.04E-03

-4.59E-01

-1.83E+00

<BR />2.30E+01

1.47E+00

-1.63E-02

0.00E+00

-3.67E-01

1.38E+00

<BR />2.40E+01

1.53E+00

-4.69E-02

2.04E-03

-4.59E-01

-1.38E+00

<BR />2.50E+01

1.60E+00

-8.36E-02

8.15E-03

-5.50E-01

-1.38E+00

<BR />2.60E+01

1.67E+00

-1.08E-01

1.43E-02

-3.67E-01

2.75E+00

<BR />2.70E+01

1.73E+00

-1.32E-01

1.63E-02

-3.67E-01

-7.58E-06

<BR />2.80E+01

1.80E+00

-1.59E-01

1.63E-02

-3.97E-01

-4.59E-01

<BR />2.90E+01

1.87E+00

-1.81E-01

1.83E-02

-3.36E-01

9.17E-01

<BR />3.00E+01

1.93E+00

-2.02E-01

2.04E-02

-3.06E-01

4.59E-01

<BR />3.10E+01

2.00E+00

-2.26E-01

2.65E-02

-3.67E-01

-9.17E-01

<BR />3.20E+01

2.07E+00

-2.41E-01

2.85E-02

-2.14E-01

2.29E+00

<BR />3.30E+01

2.13E+00

-2.47E-01

2.85E-02

-9.17E-02

1.83E+00

<BR />3.40E+01

2.20E+00

-2.59E-01

3.06E-02

-1.83E-01

-1.38E+00

<BR />3.50E+01

2.27E+00

-2.65E-01

3.06E-02

-9.17E-02

1.38E+00

<BR />3.60E+01

2.33E+00

-2.71E-01

3.06E-02

-9.17E-02

1.86E-07

<BR />3.70E+01

2.40E+00

-2.55E-01

3.06E-02

2.45E-01

5.04E+00

<BR />3.80E+01

2.47E+00

-2.43E-01

2.85E-02

1.83E-01

-9.17E-01

<BR />3.90E+01

2.53E+00

-2.32E-01

2.85E-02

1.53E-01

-4.59E-01

<BR />4.00E+01

2.60E+00

-2.20E-01

2.65E-02

1.83E-01

4.59E-01

<BR />4.10E+01

2.67E+00

-1.98E-01

2.45E-02

3.36E-01

2.29E+00

<BR />4.20E+01

2.73E+00

-1.79E-01

2.24E-02

2.75E-01

-9.17E-01

<BR />4.30E+01

2.80E+00

-1.57E-01

2.24E-02

3.36E-01

9.17E-01

<BR />4.40E+01

2.

Conclusion

As the two ends of the half-metre rule may not be marked accurately in the MVA software, the distance marked may not be exactly 0.5 m. Same as error (2), as the MVA software requires the setting of the end points of the half-metre rule as a reference to locate the displacement, the displacement at each time interval does not reflect the true value of the displacement.
The position of mass marked for each time interval may not be the same for all time intervals
It is difficult to locate the mass at the same position for each time interval, therefore the displacement obtained is not accurate for each time interval.
There may be a damping effect by air resistance
Air resistance exists, hence a damping force acts on the mass in motion, resulting in smaller and smaller amplitude obtained and also causing deviations in displacement.
The spring may not be perfectly elastic
As the spring provided may not be perfect, the whole motion may not be entirely a simple harmonic motion. The graphs obtained from the experimental results may not truly reflect the characteristics of a simple harmonic motion.

Conclusion

The velocity leads the displacement by a quarter of the cycle, and the acceleration leads the velocity also by a quarter of the cycle.

Also, the acceleration is directly proportional to displacement in a simple harmonic motion and is in an opposite direction to x.

Possible improvements of the experiment

1. A heavier mass could be used to obtain a smoother motion.
2. If possible, more trials can be done to average out the random errors and obtain a better result.

This student written piece of work is one of many that can be found in our AS and A Level Mechanics & Radioactivity section.

## Found what you're looking for?

• Start learning 29% faster today
• 150,000+ documents available
• Just £6.99 a month

Not the one? Search for your essay title...
• Join over 1.2 million students every month
• Accelerate your learning by 29%
• Unlimited access from just £6.99 per month

# Related AS and A Level Mechanics & Radioactivity essays

1. ## The acceleration of a ball down various inclines

3 star(s)

wooden support every time you change the incline, rather than buying 5 different supports. 2. Set up wooden support and place the pine wood plank on top, the end of the plank lying on the support. 3a. With helpers timing when the ball go over the intervals, hold the ball touching the inclined end, waiting for everyone to be ready.

2. ## Investigating Force, Mass and Acceleration using a Trolley

A time interval of 1 s will have +5 % error but if the time interval decreases to 0.1 s the maximum error will increase to +50 %. V) C The mass used in the experiment can also cause small errors.

1. ## CIRCULAR MOTION - revision notes and calculations

then the value of ? should be large. (2) The design of a racing track is not linear but curved upwards with ? increasing outwards because as the car is moving too fast and turnning too sharp, the car will skid outwards, the larger value of ?

2. ## Mass on a spring - and investigation into resonance

After considering the above table of errors, we amend the natural resonance of the spring recorded from the first experiment as follows:- k = 22.42 N/m +/- 7.14% = 22.42 +/- 1.60 N/m This would mean that the top end of our range is k = 24.02 N/m.

1. ## Investigating the relationship between force, mass and acceleration

The results for force and acceleration were more accurate than the results for mass and acceleration. This is possibly due to the fact that we assumed the weight of the trolley to be 1kg, when in actual fact it is probably less.

2. ## Carry out an experiment of simple harmonic motion using a simple pendulum and determine ...

Since gravity is the constant, a value for the acceleration due to gravity can be determined from the gradient. T = 2? x ?L ?g ( ( ( ( y = m x + c Where m = gradient of graph c = intercept y = vertical axis - time

1. ## OCR B Advancing Physics Physics Practical Investigation Coursework Investigating Simple Harmonic Oscillations

The pendulum exhibits simple harmonic motion, the energy being transferred between potential (at the extremes of the oscillation) and kinetic energy. However, resistive forces from friction between the string and the clamp and also the between the bob and the air, cause an exponential decrease in energy in the system.

2. ## Investigation into the factors that affect acceleration.

So we gave the experiment a test run to make sure everything worked according to plan. The test run went smoothly and so we all agreed the experiment would be a success Prediction Graph Equipment * Runway * Trolley * Metre Stick * Ticker Timer * Roll of ticker timer

• Over 160,000 pieces
of student written work
• Annotated by
experienced teachers
• Ideas and feedback to