Period and Amplitude

A 175 g mass attached to a horizontal spring oscillates at a frequency of 2.0 Hz. At one instant, the mass is at x = 5.0 cm and has vx = -32 cm/s

Determine the period.

P = 1 / f
= 1 / 2.0

T= 0.5 sec.

Determine the amplitude.

w = 2pi * f
= 2pi * 2.0
= 12.6 rad / s.
v = w √(a² – x²)
– 32 = 4π √(a² – 5.0²)

a² = [ – 32 / (4π) ]² + 5.0²
A = 5.61 cm.

Determine the maximum speed.

v_max = wa
= 70.5 cm/s.

Determine the total energy.

W_total = mv_max² / 2

= 0.175 * 0.705² / 2
= 4.35 * 10^-2 J.