## 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 √(a^{2} – x^{2})

– 32 = 4π √(a^{2} – 5.0^{2})

a^{2} = [ – 32 / (4π) ]^{2} + 5.0^{2}

A = 5.61 cm.

**Determine the maximum speed.**

v_{max} = wa

= 70.5 cm/s.

**Determine the total energy.**

W_{total} = mv_{max}^{2} / 2

= 0.175 * 0.705^{2} / 2

= 4.35 * 10^{-2} J.

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