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
3.6 kgk

A 3.6 kg mass on a spring makes 40 complete oscillations in 49 s. Find the frequency f of the oscillation.

m = 3.6 kgN = 40t = 49 s
f = Hz
2.Easy
3 kgk = 370 N/m

A 3 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 3 kgk = 370 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
mk = 70 N/mA = 17 cmx = 12 cm

A mass on a spring with k = 70 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find its kinetic energy K when it is 12 cm from equilibrium.

k = 70 N/mA = 17 cmx = 12 cm
K = J
6.Hard
1.9 kgk = 370 N/mA = 9 cm

A 1.9 kg mass on a spring with k = 370 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.9 kgk = 370 N/mA = 9 cm
E = J

Answer key

  1. 1. f = 0.8163 Hz
  2. 2. T = 0.5658 s
  3. 3. L = 1.68 m
  4. 4. L = 0.8051 m
  5. 5. K = 0.5075 J
  6. 6. E = 1.498 J

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