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
3.8 kgk = ?

A 3.8 kg mass on a spring oscillates with a period of 1.05 s. Find the spring stiffness k.

m = 3.8 kgT = 1.05 s
k = N/m
2.Easy
0.5 kgk10.5 cm

Hanging a 0.5 kg mass on a spring stretches it by 10.5 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 = 0.5 kgx = 10.5 cmg = 9.81 m/s²
T = s
3.Medium
0.9 kgk = 430 N/mA = 20 cmx = 10 cm

A 0.9 kg mass on a spring with k = 430 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 10 cm from equilibrium.

m = 0.9 kgk = 430 N/mA = 20 cmx = 10 cm
v = m/s
4.Medium
t (s)x (cm)1.35 s

A 0.7 kg mass on a spring with k = 150 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.35 s (with sign).

m = 0.7 kgk = 150 N/mA = 15 cmt = 1.35 s
x = cm
5.Hard
3.2 kgk = 50 N/mA = 3 cm

A 3.2 kg mass on a spring with k = 50 N/m is pulled 3 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.2 kgk = 50 N/mA = 3 cm
E = J
6.Hard
2.2 kgk = 260 N/m

A 2.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 260 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 2.2 kgk = 260 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. k = 136.1 N/m
  2. 2. T = 0.65 s
  3. 3. v = 3.786 m/s
  4. 4. x = 9.177 cm
  5. 5. E = 0.0225 J
  6. 6. vmax = 0.9024 m/s

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