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

Options

A. Force acting is directly proportional to displacement form 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, C

Explanation

Let us writen the equation for the `SHM`
`x = asin (omegat +phi)`
Clearly, it is a periodic motions as it involves sine function.
Let us find velocity of the particle,
`v = (dx)/(dt) = (d)/(dt) (a sin (omega +phi))`
`= a omega cos (omegat +phi)`
Velocity is also periodic because it is a cosine function.
Now let us find acceleration,
`A = (dv)/(dt) = (d^(2)x)/(dt^(2)) =- a omega^(2) sin (omegat +phi)`
The acceleration is a sine function, hence cannot be constant.
`rArr A =- (omega^(2)A) sin (omegat +phi) =- omega^(2)x`
Force, `F =` mass `xx` acceleration
`= mA =- m omega^(2) x`
Hence, force acting is directly proportional to displacement form the mean position and opposite to it.