a spring constant of N m – . The block is pulled to a distance x = cm from its equilibrium position at x = on a frictionless surface from rest at t = . Calculate the kinetic, potential and total energies of the block when it is cm away from the mean position. Answer The block executes SHM, its angular frequency, as given by Eq.
( .14b), is ω = k N m – 1kg = . rad s – Its displacement at any time t is then given by, x ( t ) = . cos ( . t ) Therefore, when the particle is cm away from the mean position, we have .
Kinetic energy, potential energy and total energy as a function of time [shown in (a)] and displacement [shown in (b)] of a particle in SHM. The kinetic energy and potential energy both repeat after a period T/ . The total energy remains constant at all t or x. let it go.
The stone executes a to and fro motion, it is periodic with a period of about two seconds. We shall show that this periodic motion is simple harmonic for small displacements from Or cos ( . t ) = . and hence sin ( .
t ) = = . Then, the velocity of the block at x = cm is = . × . × .
m s – = . m s – Hence the K.E. of the block, v = ½[1kg × ( . m s – ) ] = .
J The total energy of the block at x = cm, = K.E. + P.E. = . J we also know that at maximum displacement, K.E.
is zero and hence the total energy of the system is equal to the P.E. Therefore, the total energy of the system, = ½( N m – ×