Question #d2662

1 Answer
Jan 18, 2017

In Simple harmonic Motion of an ideal particle instantaneous mechanical energy is given by the expression

#"Mechanical Energy"E_m="Potential Energy"E_p+"Kinetic Energy"E_k#

At mean position
#"Potential Energy"=0#. Therefore all the energy is its
Kinetic energy#=E_k(max)#,
Similarly at extreme positions #"Kinetic Energy"=0#. Hence all the enrgy is its
#"Potential Energy"=E_p(max)#

The total mechanical energy remains constant instantaneously throughout the cycle. Therefore, total mechanical energy as it passes through a position that is 0.617 of the amplitude away from the equilibrium position is also equal to
#E_m(0.617)=E_p(max)=E_k(max)# ......(1)

To calculate actual value of total mechanical energy we need details of the Simple Harmonic Motion.

For example, if an ideal spring having spring constant #k# is stretched by a maximum length#=x_max#, its potential energy at extreme position is given as
#E_p(max)=1/2kx_max^2#
From equation (1) above
#E_m(0.617)=E_p(max)=1/2kx_max^2#