Question

A particle executes SHM on a line 8 cm long . Its KE and PE will be equal when its distance from the mean position is
A. 4 cm
B. 2 cm
C. `2sqrt(2)`
D. `sqrt(2)` cm

Answer 1

Correct Answer - C
Amplitude , A=4 cm
For `KE-PE implies (1)/(2)momega^(2)(A^(2)-x^(2))=(1)/(2)momega^(2)x^(2)`
`implies x^(2)=(A^(2))/(2)impliesx=(A)/(sqrt(2))`
Let x be the point , where KE=PE
Hence,`(1)/(2)momega^(2)(a^(2)-x^(2))=(1)/(2)momega^(2)x^(2)`
`2x^(2)=a^(2),x=(a)/(sqrt(2))`
`implies x=(4)/(sqrt(2))=2sqrt(2)` cm