The displacement (x) of a particle as a function of time (t) is given by
`x=asin(bt+c)`
Where a,b and c are constant of motion. Choose the correct statemetns from the following.

Options

A. The motion repeats itself in a time interval of `(2pi)/(b)`
B. The energy of the particle remains constant.
C. The velocity of the particle zero at `x=+-a`
D. The acceleration of the particle is zero at `x=+-a`

Answer

A, B, C

Explanation

The motion of the particle is simple harmonic. The displacement at time `t` is `x=asin(bt+c)`
Therefore, displacement at time `(t+((2pi)/(b)))` is
`x` at `(t+(2pi)/(b))=asin[b(t+(2pi)/(b))+c]`
`=asin[bt+c+2pi]=asin(bt+c)=x` (at time t)
Hence, statement (a) is correct. Statement (b) is also correct since the same displacement is recovered after a time interval of `((2pi)/(b))`. Statement (c ) is correct because the velocity is zero when the displacement `=+-` the amplitude. i.e, at the extreme ends of the motion. statements (d) is incorrect, the acceleration is maximum (in magnitude) at `x=+-A`.