Question

Total energy of a particle executing S.H.M of amplitude A is proportional to:

(a)A?
(b) A-2
(c) A
(d) A-​

Answer 1

If x = A sin w t where w is the angular frequency

then v = w A cos w t

Since KE = 1/2 m Vmax^2 and Vmax = w A maximum KE

the total energy is proportional to A^2

Also, since the maximum potential energy is

PEmax = 1/2 K A^2 where the KE is zero (maximum amplitude)

one can again see that the total energy is proportional to A^2