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
2.8 kgk

A 2.8 kg mass on a spring makes 30 complete oscillations in 20 s. Find the frequency f of the oscillation.

m = 2.8 kgN = 30t = 20 s
f = Hz
2.Easy
3.3 kgk = 60 N/m

A 3.3 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.3 kgk = 60 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.5 s? Use g = 9.81 m/s². Find L.

T = 1.5 sg = 9.81 m/s²
L = m
4.Medium
1.7 kgk = 110 N/mA = 12 cmx = 5 cm

A 1.7 kg mass on a spring with k = 110 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 5 cm from equilibrium.

m = 1.7 kgk = 110 N/mA = 12 cmx = 5 cm
v = m/s
5.Hard
3.5 kgk = 370 N/mA = 3 cm

A 3.5 kg mass on a spring with k = 370 N/m is pulled 3 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.5 kgk = 370 N/mA = 3 cm
amax = m/s²
6.Hard
mk = 190 N/mA = 5 cmx = 1 cm

A mass on a spring with k = 190 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find the energy U stored in the spring when the mass is 1 cm from equilibrium.

k = 190 N/mA = 5 cmx = 1 cm
U = J

Answer key

  1. 1. f = 1.5 Hz
  2. 2. f = 0.6786 Hz
  3. 3. L = 0.5591 m
  4. 4. v = 0.8775 m/s
  5. 5. amax = 3.171 m/s²
  6. 6. U = 0.0095 J

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