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
1.4 kgk = 200 N/m

A 1.4 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 1.4 kgk = 200 N/m
T = s
2.Easy
3 kgk = 20 N/m

A 3 kg mass on a spring with stiffness 20 N/m oscillates on a frictionless surface. Find the period T.

m = 3 kgk = 20 N/m
T = s
3.Medium
2.9 kgk = 20 N/mA = 7 cmx = 4 cm

A 2.9 kg mass on a spring with k = 20 N/m oscillates on a frictionless surface with an amplitude of 7 cm. Find its speed v when it is 4 cm from equilibrium.

m = 2.9 kgk = 20 N/mA = 7 cmx = 4 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.5 s? Use g = 9.81 m/s². Find L.

T = 2.5 sg = 9.81 m/s²
L = m
5.Hard
1.5 kgk = 290 N/mA = 11 cm

A 1.5 kg mass on a spring with k = 290 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 290 N/mA = 11 cm
E = J
6.Hard
mk = 250 N/mA = 12 cmx = 8 cm

A mass on a spring with k = 250 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its kinetic energy K when it is 8 cm from equilibrium.

k = 250 N/mA = 12 cmx = 8 cm
K = J

Answer key

  1. 1. T = 0.5257 s
  2. 2. T = 2.433 s
  3. 3. v = 0.1509 m/s
  4. 4. L = 1.553 m
  5. 5. E = 1.754 J
  6. 6. K = 1 J

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