Which of the following statements is/are true for a simple harmonic oscillator ?

Options

A. (a) Force acting is directly porportional to displacement from the mean postion and opposite to it
B. Motion is periodic
C. Acceleration of the oscillator is constant
D. The velocity is periodic

Answer

A:B:D

Explanation

Let the equation for the SHM is `x=asinomegat`. ltbr gt Clearly, it is a periodic motion because it involves sine functon.
Velocity `v=(dx)/(dt)=(d)/(dt)"(asinomegat)=aomegacosomegat`
Velocity is also periodic because of cosine function.
Acceleration, `A=(dv)/(dt)=(d^(2)x)/(dt^(2))=-aomega^(2)sinomegat`
[:' Acceleration is a sine function, hence cannot be constant]
`=-(omega^(2)a)sinomegat=-omega^(2)x`
Force, `F="massxx acceleration"`
`=mA=-momega^(2)x`
Hence, force acting is directly porportioal to displacement from the mean position and oppsite to it.