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
2.2 kgk = 10 N/m

A 2.2 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the period T.

m = 2.2 kgk = 10 N/m
T = s
2.Easy
1.1 kgk = 60 N/m

A 1.1 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.1 kgk = 60 N/m
f = Hz
3.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
4.Medium
2.9 kgk = 290 N/mA = 11 cmx = 10 cm

A 2.9 kg mass on a spring with k = 290 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 10 cm from equilibrium.

m = 2.9 kgk = 290 N/mA = 11 cmx = 10 cm
v = m/s
5.Hard
mk = 270 N/mA = 10 cmx = 4 cm

A mass on a spring with k = 270 N/m oscillates on a frictionless surface with an amplitude of 10 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 270 N/mA = 10 cmx = 4 cm
U = J
6.Hard
0.3 kgk = 450 N/mA = 15 cm

A 0.3 kg mass on a spring with k = 450 N/m is pulled 15 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.3 kgk = 450 N/mA = 15 cm
amax = m/s²

Answer key

  1. 1. T = 2.947 s
  2. 2. f = 1.175 Hz
  3. 3. T = 3.108 s
  4. 4. v = 0.4583 m/s
  5. 5. U = 0.216 J
  6. 6. amax = 225 m/s²

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