Question

Calculate the ratio of displacement to amplitude when kinetic energy of the body executing shm is thrice the potential energy

Answer 1

Answer:

Ratio of displacement to amplitude is 2 : 1

Explanation:

Given: K.E. = 3 P.E.

To find : x/A

Formula:

I) K.E. = 1/2 k ( A^2-x^2)

II) P.E. = 1/2 k x^2

Calculation:

K.E. = 3 P.E. ....(given)

using formula (I) & (II)

1/2 k ( A^2-x^2) = 3 (1/2 k x^2)

A^2-x^2 = 3 x^2

A^2 = 3 x^2 + x^2

A^2 = 4x^2

√(A^2) = √( 4x^2)

A = 2x

x/A = 2x/A

therefore, x:A = 2 : 1