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
3.5 kgk = ?

A 3.5 kg mass on a spring makes 25 complete oscillations in 14 s. Find the spring stiffness k.

m = 3.5 kgN = 25t = 14 s
k = N/m
2.Easy
2.5 kgk11 cm

Hanging a 2.5 kg mass on a spring stretches it by 11 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 = 2.5 kgx = 11 cmg = 9.81 m/s²
T = s
3.Medium
3 kgk = 440 N/mA = 9 cmx = 5 cm

A 3 kg mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 9 cm. Find its speed v when it is 5 cm from equilibrium.

m = 3 kgk = 440 N/mA = 9 cmx = 5 cm
v = m/s
4.Medium
1.9 kgk = 420 N/mA = 4 cmx = 3 cm

A 1.9 kg mass on a spring with k = 420 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 3 cm from equilibrium.

m = 1.9 kgk = 420 N/mA = 4 cmx = 3 cm
v = m/s
5.Hard
0.5 kgk = 80 N/mA = 16 cm

A 0.5 kg mass on a spring with k = 80 N/m is pulled 16 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.5 kgk = 80 N/mA = 16 cm
E = J
6.Hard
2.8 kgk = 260 N/mA = 2 cm

A 2.8 kg mass on a spring with k = 260 N/m is pulled 2 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.8 kgk = 260 N/mA = 2 cm
E = J

Answer key

  1. 1. k = 440.6 N/m
  2. 2. T = 0.6653 s
  3. 3. v = 0.9063 m/s
  4. 4. v = 0.3934 m/s
  5. 5. E = 1.024 J
  6. 6. E = 0.052 J

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