A brick of mass 4 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is then stretched an additional 2 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g=980 cm/s^2.

Set up a differential equation with initial conditions describing the motion and solve it for the displacement s (t) of the mass from its equilibrium position (with the spring stretched 3 cm).

Question

Honeybun

Physics

10 April, 13:40

A brick of mass 4 kg hangs from the end of a spring. When the brick is at rest, the spring is stretched by 3 cm. The spring is then stretched an additional 2 cm and released. Assume there is no air resistance. Note that the acceleration due to gravity, g, is g=980 cm/s^2.

Set up a differential equation with initial conditions describing the motion and solve it for the displacement s (t) of the mass from its equilibrium position (with the spring stretched 3 cm).

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Juliet Henry · Answer 1

Let s be displacement from equilibrium position. Restoring force

m d²s / dt² = - k s

d²s / dt² = - k / m s

Put k / m = ω

d²s / dt² + ω² s = 0

The solution of this differential equation

= s = A cosωt

Now when t = 0, s = 2 cm

A = 2 cm

Putting the values we have

2 = A cos 0

A = 2 cm

s (t) = 2 cos ωt