


1. 

An object oscillates with s.h.m. of time period
4s. 

a) 
Calculate the magnitude of the constant which relates the
acceleration of the object to its displacement 

b) 
Calculate the acceleration when the displacement is
2×10^{2}m. 



2. 

During a simple harmonic oscillation, the acceleration is
4cms^{2} when the
displacement is 5cm. 


Calculate the time period. 



3. 

A point is moving with s.h.m. of time period 10s
and amplitude 15cm. 


At t=0 the displacement is 0. 


Calculate the displacement at t=2s 



4. 

A body is moving with s.h.m. of time period 0.2s
and amplitude 1cm. 


At t=0 the body is at its
equilibrium position. 

a) 
Calculate the first time (after t=0)
at which the mass will be 0.5cm from
its equilibrium position 

b) 
Calculate the next time at which it will have the same
displacement. 



5. 

A body is moving with s.h.m. of time period
5s and amplitude 0.4m. 


At t=0 the body is at its
equilibrium position. 

a) 
Calculate the maximum speed of the object 

b) 
Calculate the speed at time t=2s. 

c) 
At t=2s, is the object moving
towards or away from the equilibrium position? 



6. 

A body oscillates with s.h.m. with a
frequency of 100Hz. 


At t=0 it is at the equilibrium
position. 


What is speed of the body at t=2.5×10^{3}s? 



7. 

An object of mass 0.5kg moves
with s.h.m. of time period 1.5s and
amplitude 5×10^{3}m. 

a) 
Calculate the value of the constant k (the force per unit
displacement) for this motion 

b) 
Calculate the restoring maximum force which acts on the mass
(assume there are no other forces acting on it). 



8. 

Describe (briefly) the energy changes which take place when 

a) 
a pendulum oscillates in air 

b) 
a mass oscillates (vertically) on a spring, in a vacuum. 



9. 

On the earth, a pendulum has a time period of 1.5s
and a mass/spring oscillator has a
time period 0.8s. 


If both these objects were taken to the moon, what would their
time periods be? 


Take the acceleration due to gravity on the moon to be g/6 



10. 

A pendulum has a bob of mass 0.2kg. 


It has a length of 0.5m. 


Ignoring the effects of air resistance, calculate 

a) 
the maximum kinetic energy of the bob given that the initial
displacement from the equilibrium position is 0.2m 

b) 
the total energy of this oscillation. 