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
4.3 kgk = 290 N/m

A 4.3 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the period T.

m = 4.3 kgk = 290 N/m
T = s
2.Easy
0.7 kgk = 160 N/m

A 0.7 kg mass on a spring with stiffness 160 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 160 N/m
T = s
3.Medium
1.9 kgk = 370 N/mA = 5 cmx = 3 cm

A 1.9 kg mass on a spring with k = 370 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 3 cm from equilibrium.

m = 1.9 kgk = 370 N/mA = 5 cmx = 3 cm
v = m/s
4.Medium
t (s)x (cm)1 s

A 2.3 kg mass on a spring with k = 190 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1 s (with sign).

m = 2.3 kgk = 190 N/mA = 3 cmt = 1 s
x = cm
5.Hard
2.6 kgk = 30 N/mA = 8 cm

A 2.6 kg mass on a spring with k = 30 N/m is pulled 8 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.6 kgk = 30 N/mA = 8 cm
E = J
6.Hard
mk = 160 N/mA = 11 cmx = 10 cm

A mass on a spring with k = 160 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find the energy U stored in the spring when the mass is 10 cm from equilibrium.

k = 160 N/mA = 11 cmx = 10 cm
U = J

Answer key

  1. 1. T = 0.7651 s
  2. 2. T = 0.4156 s
  3. 3. v = 0.5582 m/s
  4. 4. x = −2.832 cm
  5. 5. E = 0.096 J
  6. 6. U = 0.8 J

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