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
0.6 kgk = 380 N/m

A 0.6 kg mass on a spring with stiffness 380 N/m oscillates on a frictionless surface. Find the period T.

m = 0.6 kgk = 380 N/m
T = s
2.Easy
3.1 kgk = 80 N/m

A 3.1 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the period T.

m = 3.1 kgk = 80 N/m
T = s
3.Medium
L = 2.9 m

A simple pendulum has a length of 2.9 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.9 mg = 9.81 m/s²
T = s
4.Medium
1.4 kgk = 410 N/mA = 16 cmx = 14 cm

A 1.4 kg mass on a spring with k = 410 N/m oscillates on a frictionless surface with an amplitude of 16 cm. Find its speed v when it is 14 cm from equilibrium.

m = 1.4 kgk = 410 N/mA = 16 cmx = 14 cm
v = m/s
5.Hard
1.1 kgk = 290 N/mA = 14 cm

A 1.1 kg mass on a spring with k = 290 N/m is pulled 14 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.1 kgk = 290 N/mA = 14 cm
amax = m/s²
6.Hard
3.9 kgk = 310 N/mA = 14 cm

A 3.9 kg mass on a spring with k = 310 N/m is pulled 14 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.9 kgk = 310 N/mA = 14 cm
E = J

Answer key

  1. 1. T = 0.2497 s
  2. 2. T = 1.237 s
  3. 3. T = 3.416 s
  4. 4. v = 1.326 m/s
  5. 5. amax = 36.91 m/s²
  6. 6. E = 3.038 J

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