The maximum potential energy of a spring system (mass 15 kg, spring constant 850 N/m) is 6.5 J. a) What is the amplitude of the oscillation? b) What is the maximum speed? c) Setting φ = 0, write the equation for the potential energy as a function of time.

a) 0.124 m

b) 0.93 ms⁻¹

c) 0.5 k A² cos ² (ωt)

Explanation:

1) Potential energy = U = 0.5 k A², where A is the amplitude and k = 850 N/m is the spring constant.

0.5 (850) (A²) = 6.5

⇒ A = 0.124 m = Amplitude.

b) From energy conservation, 0.5 m v² = 6.5

⇒ speed = v = 0.93 ms⁻¹

c) If x = A cos ωt,

Potential energy = 0.5 k A² = 0.5 k A² cos ² (ωt)