What is its maximum speed?

Question

A point of mass performs a harmonic oscillating motion with an amplitude of 0.5 centimeters. The vibration

the duration is 1/10 second. What is its maximum speed?

Answer 1

Let

A = 0.5 cm = 5 x 10^-3m be the amplitude

T = 10^-1 s be the period,

m (unknown) be the mass,

k (unknown) be the spring constant,

v (to be calculated) be the maximum speed.

We use conservation of energy:

The spring energy, kA²/2, when the spring is at its maximum extension,

equals the kinetic energy mv²/2, when the spring passes its equilibrium position.

mv²/2 = kA²/2

v = A√(k/m)

The quantity √(k/m) can be calculated from the formula for period

T = 2π√(m/k)

√(k/m) = 2π/T

Substituting into the formula for v:

v = A√(k/m) = 2πA/T

Substituting actual numbers

v = 2π x 5 x 10-3 m / 10-1 s = 0.314 m/s