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
1.1 kgk = ?

A 1.1 kg mass on a spring oscillates with a period of 2.35 s. Find the spring stiffness k.

m = 1.1 kgT = 2.35 s
k = N/m
2.Easy
2.1 kgk = ?

A 2.1 kg mass on a spring oscillates with a period of 1.4 s. Find the spring stiffness k.

m = 2.1 kgT = 1.4 s
k = N/m
3.Medium
L = 1.8 m

A simple pendulum has a length of 1.8 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.8 mg = 9.81 m/s²
T = s
4.Medium
L = 2.4 m

A simple pendulum has a length of 2.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.4 mg = 9.81 m/s²
T = s
5.Hard
0.8 kgk = 340 N/mA = 16 cm

A 0.8 kg mass on a spring with k = 340 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.8 kgk = 340 N/mA = 16 cm
amax = m/s²
6.Hard
1.5 kgk = 500 N/m300 m/s

A 20 g bullet moving at 300 m/s hits and stays in a 1.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 500 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 300 m/sM = 1.5 kgk = 500 N/m
A = cm

Answer key

  1. 1. k = 7.864 N/m
  2. 2. k = 42.3 N/m
  3. 3. T = 2.691 s
  4. 4. T = 3.108 s
  5. 5. amax = 68 m/s²
  6. 6. A = 21.76 cm

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