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
2.2 kgk = 80 N/m

A 2.2 kg mass on a spring with stiffness 80 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.2 kgk = 80 N/m
f = Hz
2.Easy
3.6 kgk

A 3.6 kg mass on a spring makes 20 complete oscillations in 38 s. Find the frequency f of the oscillation.

m = 3.6 kgN = 20t = 38 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
1.4 kgk = 300 N/mA = 12 cmx = 1 cm

A 1.4 kg mass on a spring with k = 300 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 1 cm from equilibrium.

m = 1.4 kgk = 300 N/mA = 12 cmx = 1 cm
v = m/s
5.Hard
1.9 kgk = 70 N/mA = 16 cm

A 1.9 kg mass on a spring with k = 70 N/m is pulled 16 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.9 kgk = 70 N/mA = 16 cm
amax = m/s²
6.Hard
3.1 kgk = 480 N/mA = 9 cm

A 3.1 kg mass on a spring with k = 480 N/m is pulled 9 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.1 kgk = 480 N/mA = 9 cm
vmax = m/s

Answer key

  1. 1. f = 0.9597 Hz
  2. 2. f = 0.5263 Hz
  3. 3. L = 0.159 m
  4. 4. v = 1.751 m/s
  5. 5. amax = 5.895 m/s²
  6. 6. vmax = 1.12 m/s

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