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