NUMERICALS ON SIMPLE HARMONIC MOTION

1. A simple harmonic motion is represented by by    x = 10 sin (20t + 0.5), 

Write down its amplitude, angular frequency, frequency, time period and initial phase if displacement is measured in in metres and time in seconds. 

2. A body oscillates with SHM according to the equation, 

x = (5.0 m) cos [(2π rad/s)t + π/4]

At t = 1.5 s, calculate (a) displacement, (b) speed and (c) acceleration of the body. 

3. The equation of a simple harmonic motion is given by , 

y = 6 sin 10π t + 8 cos 10π t, where y is in cm, and t in seconds. Determine the amplitude, period and initial phase. 

4. A body oscillates with SHM according to the equation :

x(t) = 5 cos (2 πt + π/4)

Where t is in second, and x in metres. Calculate, 

(a) displacement at t = 0

(b) time period, (c) initial velocity

5. A spring of force constant  800 N/m has an extension of 5 cm. What is the work done in increasing the extension from 5 to 15 cm?

6. A body executes SHM of time period 8 s. If its mass be 0.1 kg, its velocity 1 second after it passes through its mean position be 4 m/s, find its (i) kinetic energy (ii) potential energy and (iii) total energy. 

7. A particle is executing SHM of amplitude A. At what displacement from the mean position, is the energy half kinetic and half potential?

8. What is the length of a second pendulum? 

(A second pendulum is a pendulum with a time period of 2 s).