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
3.4 kgk = 170 N/m

A 3.4 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the period T.

m = 3.4 kgk = 170 N/m
T = s
2.Easy
2 kgk

A 2 kg mass on a spring makes 30 complete oscillations in 60 s. Find the frequency f of the oscillation.

m = 2 kgN = 30t = 60 s
f = Hz
3.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
4.Medium
L = 1.4 m

A simple pendulum has a length of 1.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.4 mg = 9.81 m/s²
T = s
5.Hard
1.2 kgk = 250 N/mA = 8 cm

A 1.2 kg mass on a spring with k = 250 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.2 kgk = 250 N/mA = 8 cm
amax = m/s²
6.Hard
2 kgk = 1600 N/m200 m/s

A 12 g bullet moving at 200 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1600 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 200 m/sM = 2 kgk = 1600 N/m
A = cm

Answer key

  1. 1. T = 0.8886 s
  2. 2. f = 0.5 Hz
  3. 3. T = 1.554 s
  4. 4. T = 2.374 s
  5. 5. amax = 16.67 m/s²
  6. 6. A = 4.23 cm

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