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  8 Simple Harmonic Motion

Objective Questions 

  1. The displacement–time graph of a particle in simple harmonic motion is as shown.

  Which of the following is the graph of velocity v against time t ?

A C

B D

  2. The force on a body of mass m which is in simple harmonic motion is given by

F  = –ky

  where k  is a constant and  y is the displacement from a fixed point O.  Which of the following is the angular frequency of the motion?

A k Cm—k 

 

B k   Dk —m

  3. The figure shows a simple pendulum of length l.

Which of the following is the magnitude of the angular acceleration of the pendulum bob

when the string makes an angle of θ  to the vertical?

Al—g θ C l —g θ 

Bg

—

lθ D

g

—

lθ 

0T  2T 

Time

Displacement

T 

v 

2T 

0T 

v 

2T t 

t T 

v 

2T t 

0

0 0

T 

v 

2T t 

θ 

l

QB AA STPM Phys V1 C8 4th indd 1QB AA STPM Phys V1 C8 4th.indd 1 3/7/2008 5:00:14 PM3/7/2008 5:00:14 PM

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  4. When a mass is hung from the lower end of a vertical spring of natural length L, the spring

extends by a length of a. The mass is then displaced downwards so that the total extension

in the spring is 1.5a, and is then released.

 

If the acceleration due to gravity is g, the maximum acceleration of the mass is

Ag

—–1.5

Bg—2

 

C2

—3 g

D3g—–2

  5. Which of the following quantities is constant for a body in simple harmonic motion?

A Acceleration

B Velocity

C Force on the body

D Angular frequency

Structured Question 

  1. (a) When a 200 g mass is suspended from the lower end of a vertical spring, the spring

extends by 4.0 cm. What is the force constant of the spring?(b) Two springs that are identical to the spring in (a) are joined in series and a 400 g mass

is suspended from the lower end of the combined spring.

  (i) What is the value of the force constant of the combined spring?

  (ii) When the 400 g mass is slightly displaced, it oscillates vertically. Calculate the

frequency of oscillation.

Essay Question 

  1. (a) What is meant by ‘a body is moving in simple harmonic motion’?

(b) One end of a helical spring is fixed and a 0.25 kg mass on a smooth horizontal surface

is attached to the other end. The mass is displaced through a distance of 0.15 m from

the equilibrium position by a force of 36 N and then released. The mass performs simple

harmonic motion.Calculate

  (i) the period of the simple harmonic motion

 (ii) the displacement of the mass 0.080 s after being released

 (iii) the kinetic energy of the mass 0.080 s after being released

 (iv) the potential energy of the spring 0.080 s after the mass is released.

(c) Sketch a graph to show the variation of

(i) kinetic energy of the mass

(ii) potential energy of the spring

with displacement  x  from the equilibrium position.

L

a 1.5a

L

m 

m 

QB AA STPM Phys V1 C8 4th indd 2QB AA STPM Phys V1 C8 4th.indd 2 3/7/2008 5:00:16 PM3/7/2008 5:00:16 PM