Springs & pendulums worksheet with answers

Free printable Springs & pendulums worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy
2.4 kgk7.5 cm

Hanging a 2.4 kg mass on a spring stretches it by 7.5 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 2.4 kgx = 7.5 cmg = 9.81 m/s²
T = s
2.Easy
1.5 kgk

A 1.5 kg mass on a spring makes 30 complete oscillations in 19 s. Find the frequency f of the oscillation.

m = 1.5 kgN = 30t = 19 s
f = Hz
3.Medium
0.3 kgk = 50 N/mA = 4 cmx = 2 cm

A 0.3 kg mass on a spring with k = 50 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 2 cm from equilibrium.

m = 0.3 kgk = 50 N/mA = 4 cmx = 2 cm
v = m/s
4.Medium
1.5 kgk = 240 N/mA = 7 cmx = 2 cm

A 1.5 kg mass on a spring with k = 240 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its speed v when it is 2 cm from equilibrium.

m = 1.5 kgk = 240 N/mA = 7 cmx = 2 cm
v = m/s
5.Hard
4 kgk = 700 N/m400 m/s

A 12 g bullet moving at 400 m/s hits and stays in a 4 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 700 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 400 m/sM = 4 kgk = 700 N/m
A = cm
6.Hard
2.8 kgk = 360 N/mA = 16 cm

A 2.8 kg mass on a spring with k = 360 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.8 kgk = 360 N/mA = 16 cm
amax = m/s²

Answer key

  1. 1. T = 0.5494 s
  2. 2. f = 1.579 Hz
  3. 3. v = 0.4472 m/s
  4. 4. v = 0.8485 m/s
  5. 5. A = 9.058 cm
  6. 6. amax = 20.57 m/s²

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