# A string is stretched so that its length is increased by 1/x of its original length.The ratio of fundamental frquency of transverse vibration to that of fundamental frequency of longitude vibration will be:-

Arun
25750 Points
6 years ago

Kinetic energy in simple harmonic motion is the energy possessed by the particle by virtue of its motion.
The maximum kinetic energy in simple harmonic motion is defined as,
(K) max = ½ mw2r2 …… (1)
Where m is the mass of the body, w is the angular frequency of the oscillation and r is the amplitude of the oscillation.
But kinetic energy K is defined as,
K = ½ mv2 …... (2)
Where m is the mass of the body and v is the velocity of the body.
Substitute equation (2) in equation (1),
½ mv2 = ½ mw2r2
So, v = wr …… (3)
From equation (3) we observed that, since mass (m) is not the fundamental property of the pendulum, therefore keeping mass as a constant quantity, you have to double either frequency of the previous angular frequency of oscillation w or amplitude of the oscillation r to double the maximum speed of the oscillating object.