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
2.9 kgk = 210 N/m

A 2.9 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.9 kgk = 210 N/m
f = Hz
2.Easy
3 kgk = 260 N/m

A 3 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3 kgk = 260 N/m
f = Hz
3.Medium
1.5 kgk = 130 N/mA = 18 cmx = 7 cm

A 1.5 kg mass on a spring with k = 130 N/m oscillates on a frictionless surface with an amplitude of 18 cm. Find its speed v when it is 7 cm from equilibrium.

m = 1.5 kgk = 130 N/mA = 18 cmx = 7 cm
v = m/s
4.Medium
L = 2.3 m

A simple pendulum has a length of 2.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 2.3 mg = 9.81 m/s²
T = s
5.Hard
2.2 kgk = 440 N/mA = 14 cm

A 2.2 kg mass on a spring with k = 440 N/m is pulled 14 cm from equilibrium and released. Find its maximum speed vmax.

m = 2.2 kgk = 440 N/mA = 14 cm
vmax = m/s
6.Hard
1 kgk = 310 N/mA = 8 cm

A 1 kg mass on a spring with k = 310 N/m is pulled 8 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1 kgk = 310 N/mA = 8 cm
amax = m/s²

Answer key

  1. 1. f = 1.354 Hz
  2. 2. f = 1.482 Hz
  3. 3. v = 1.544 m/s
  4. 4. T = 3.042 s
  5. 5. vmax = 1.98 m/s
  6. 6. amax = 24.8 m/s²

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