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### S H M.

posted Apr 12, 2016, 10:24 PM by Upali Salpadoru   [ updated Jul 11, 2016, 5:39 PM ] Simple Harmonic Motion

Fig.1  Mum pushing a baby.

Mum has pushed her child! Will the baby be back?

Yes,  the baby will be back soon. What force brings her back?

Let us illustrate the problem.

This is a diagram to explain the swinging action of the baby.

At position  A.

This is the starting position. The push (yellow) is optional. The swing can work without a push. If the push is regular  the motion does not amount to simple harmonic motion.

There are two forces acting on the baby.

Fig.2 Motion of a swing analysed.

1.  The weight due to the gravitational attraction of the Earth.

2.  The tension force of the rope , without which the baby will go down directly.

What results is due to these two forces.( The push is optional.) The body moves to the position B as shown by the white curve.

Kinetic energy – zero,    Potential energy = m g h.

At position B

This is the equilibrium position. (Resting position)   As the mass is coming down with an acceleration due to gravity there will be a high velocity.    Kinetic energy- Maximum,     Potential energy – zero.

At position C

This is the highest level it can ascend.  The height will be the same as for the starting height provided there was no push and the air resistance was negligible.

Velocity-  zero,   Kinetic energy- zero.    Potential energy- maximum.

This type of motion is what the physicists say  --SIMPLE HARMONIC MOTION. Can you think of a few more examples of SHM?

Most of the periodic motions can  be included in this category of motion.

Fig. 3 Vertical oscillation of a spring.

A load is attached to a spring to swing up and down. Where ever the load is , it is a;ways pulled towards the equilibrium position. This is a crucial point in this type of motion.

In this experiment a marker is attached to the load and a paper tape is pulled to the right to get the position of the load continuously.  Then you get a wave pattern as shown in white.

One crest and one trough will give one complete cycle. The diagram shows one and a half cycles.

The time taken for a single cycle is called the period.

Frequency is the number cycles in one second.

To and fro motions, Oscillations, Vibrations, are a few of these in addition to swinging..

Here are a few characteristics of this phenomenon.

1.  The motion will be in the form of cycles that will go on repeating for some time. Fig. 2 shows only a half of the cycle.

2.  For each example there will be a frequency of completing the number of cycles in one second.

3.  As the mass moves away from the equilibrium position , there will be a restoring force acting against it.

Fig.4  Diagram for Q 1.0.

A,B  C and D  are 4 positions of a horizontally oscillating object with negligible friction. There is a spring on either side.  A is the equilibrium position.

i. At the three positions state what happens to each spring in table 1.:

ii. Complete table 2 with respect to positions of A,B and C.

Table 1.

 Position Spring . 1 Spring.2 A B C D

Table 2.

 Velocity(Magnitude and direction.) Kinetic energy Potential energy A B C D

.

Table 1.

 Position Spring . 1 Spring.2 A Relaxed Relaxed. B Pulled Compressed. C Compressed Pulled.

Table 2.

 Velocity (Magnitude and direction.) Kinetic energy Potential energy A Resting position. Zero Zero. B Zero -about to turn. Zero Maximum C Zero- about to turn. Zero Maximum D Right maximum zero. Q. 1.0 The diagram shows the fluctuation of the sea level on a particular day in Wellington. This is a simplified version from tidal data obtained from Met Service.Considering this as simple harmonic motion answer the following<-

1. What letters indicate the high tide?

a- A,D,F.   b.-  B, E.    c- B,C,E    d-  D only.

1. What is the time between two similar tides?

a- 3 hrs.    b- 6 hrs.  c- 12 hrs  d- .24 hrs,

1. Considering this to be SHM, what is the unit you may give to the time between two similar tides?

a.  Period,  b, Frequency, c,  Wavelength  d.  Cycle.

1. If the red circle stands for a particle of water , which way will it be moving?

a.  Up along the blue line .   b  Upwards  c.  Down, d. down along the blue line.

5.  What letter is closest to the mean sea level?

a- F,   b- E,   c-   D    d- C.

6. What is the amplitude of motion?

a -  1.7 m,   b,   0.85m   c-    6 hrs,    d-   12 n

(5x6=30 marks)

Q. 2.0

Out these activities which can be considered as, at least approximations to simple harmonic motion.

i.  Swinging of a chandelier.

ii. Movement of a palm tree due to wind.

iii. A child jumping up and down on a bed.

iv. Plucking a string in a guitar.

v. A clown juggling a few balls.

.

This shows a section of a typical ECG.  Electrocardiograph shows how the electric charges change in the heart muscles.

A section of a Electrocardiograph. ECG                                                (4x7=28 marks)

Q. 3.0 Some water added to this u-shaped tube is oscillating. A piece of wood, 10g. mass is floating on one arm.

i. What is the maximum potential energy on the piece of wood.

ii. What is the maximum speed it can achieve?

iii. What will be the velocity at C?

iv.  Will there be a force acting at C, and if so in which direction?

v. Find the period and frequency.

vi. Do you consider this motion as SHM? Give at least one reason to support your answer.

(5x6=30 marks)

A car tyre rolls to and fro on a curved platform. The dimensions are given in meters.

i. Describe the energy changes from start to climbed up position on the other side.

ii.  Find the highest velocity of the tyre.

iii. At which point will the highest velocity be.