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
0.4 kgk5 cm

Hanging a 0.4 kg mass on a spring stretches it by 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 = 0.4 kgx = 5 cmg = 9.81 m/s²
T = s
2.Easy
3 kgk = 10 N/m

A 3 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3 kgk = 10 N/m
f = Hz
3.Medium
3.5 kgk = 230 N/mA = 12 cmx = 3 cm

A 3.5 kg mass on a spring with k = 230 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 3 cm from equilibrium.

m = 3.5 kgk = 230 N/mA = 12 cmx = 3 cm
v = m/s
4.Medium
L = 0.6 m

A simple pendulum has a length of 0.6 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.6 mg = 9.81 m/s²
T = s
5.Hard
3 kgk = 1300 N/m350 m/s

A 15 g bullet moving at 350 m/s hits and stays in a 3 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1300 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 15 gv = 350 m/sM = 3 kgk = 1300 N/m
A = cm
6.Hard
0.7 kgk = 170 N/mA = 2 cm

A 0.7 kg mass on a spring with k = 170 N/m is pulled 2 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.7 kgk = 170 N/mA = 2 cm
amax = m/s²

Answer key

  1. 1. T = 0.4486 s
  2. 2. f = 0.2906 Hz
  3. 3. v = 0.9419 m/s
  4. 4. T = 1.554 s
  5. 5. A = 8.386 cm
  6. 6. amax = 4.857 m/s²

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