Question

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Answer 1

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Answer 2

Answer:

Given:

Equation of motion of an object in SHM is given as follows :

a = - bx

where a ----> acceleration of the body

and x -----> displacement from mean position and

b -----> arbitrary constant.

To find:

Time period of the Oscillatory object

Concept:

First of all, we need to convert this accelerated equation of SHM to the force equation. From there we can directly calculate the Time period based on formulas.

a = - bx

=> F = ma = - m × b × x

=> F = - (mb) x ............(1)

Calculation:

Time period is given by the following formula :

T = 2π√(m/k)

where m is the mass of the object,

k -----> arbitrary constant of a standard SHM Equation ( F = - kx )

Continuing with the Calculation :

T = 2π√(m/k)

=> T = 2π √(m/mb) ......[as k = mb]

=> T = 2π√(1/b)

Final answer is T = 2π√(1/b).