Question

One particle moves in simple harmonic with a period of 2 seconds and amplitude 3 cm. After swinging for 10 laps, the amplitude decreases to 2.5 cm. Find the constant for retardatio

Answer 1

Since the amplitude of the particle is reduced(damped) by some force, the particle is having a damped harmonic oscillation.

An example of a damped harmonic oscillation.

Differential equation for a damped harmonic motion is given by,

Here,

'x' is the displacement of the particle from equilibrium position

'c' is the constant of damping(retardation)

'k' is the spring constant

Motion of the particle can be graphically represented as:

Force that keeps the particle in simple harmonic motion, F_SHM = ma

(F_SHM = - kx, in the above illustration)

Force that damps(retards) the motion, F_RET = - cv = c dx/dt

Time period of a simple harmonic motion,

Substituting in SHM equation, we get

In the given example, x = 3 cm, dx = 0.5 cm, dt = 2 s, T = 2 s

Substituting,

Constant of retardation can be found with this equation by substituting values of pi and m.