Consider the following statements. The total energy of a particle executing simple harmonic motion depends on its
(1) Amplitude
(2) Period
(3) Displacement Of these statements

Options

A. I and II are correct
B. II and III are correct
C. I and III are correct
D. I, II and III are correct

Answer

A

Explanation

Potential energy of particle in SHM,
`U=(1)/(2)m omega^(2)x^(2) rArr U = 2 pi^(2) mf^(2)x^(2)" "...(i)`
Kinetic energy of particle in SHM,
`K = (1)/(2)m omega^(2)(A^(2)-x^(2))`
`rArr" "K = 2 pi^(2)mf^(2)(A^(2)-x^(2))" "...(ii)`
Hence, total energy
`E = K + U = 2 pi^(2)mf^(2)x^(2) + 2 pi^(2)mf^(2)(A^(2)-x^(2))`
`= 2pi^(2)mf^(2)A^(2)=(2pi^(2)mA^(2))/(T^(2))" "(because T = (1)/(f))`
Thus, it is obvious that total energy of particle executing simple harmonic motion depends on amplitude (A) and period (T).