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
0.7 kgk = ?

A 0.7 kg mass on a spring makes 50 complete oscillations in 52 s. Find the spring stiffness k.

m = 0.7 kgN = 50t = 52 s
k = N/m
2.Easy
1.5 kgk = 250 N/m

A 1.5 kg mass on a spring with stiffness 250 N/m oscillates on a frictionless surface. Find the period T.

m = 1.5 kgk = 250 N/m
T = s
3.Medium
L = 0.7 m

A simple pendulum has a length of 0.7 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.7 mg = 9.81 m/s²
T = s
4.Medium
3.3 kgk = 30 N/mA = 19 cmx = 13 cm

A 3.3 kg mass on a spring with k = 30 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find its speed v when it is 13 cm from equilibrium.

m = 3.3 kgk = 30 N/mA = 19 cmx = 13 cm
v = m/s
5.Hard
0.2 kgk = 260 N/mA = 8 cm

A 0.2 kg mass on a spring with k = 260 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.2 kgk = 260 N/mA = 8 cm
amax = m/s²
6.Hard
0.9 kgk = 340 N/mA = 7 cm

A 0.9 kg mass on a spring with k = 340 N/m is pulled 7 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.9 kgk = 340 N/mA = 7 cm
E = J

Answer key

  1. 1. k = 25.55 N/m
  2. 2. T = 0.4867 s
  3. 3. T = 1.678 s
  4. 4. v = 0.4178 m/s
  5. 5. amax = 104 m/s²
  6. 6. E = 0.833 J

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