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
3.4 kgk = 220 N/m

A 3.4 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.4 kgk = 220 N/m
f = Hz
2.Easy
4.3 kgk = 370 N/m

A 4.3 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the period T.

m = 4.3 kgk = 370 N/m
T = s
3.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)1.3 s

A 3.1 kg mass on a spring with k = 100 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.3 s (with sign).

m = 3.1 kgk = 100 N/mA = 6 cmt = 1.3 s
v = m/s
5.Hard
1.4 kgk = 70 N/mA = 4 cm

A 1.4 kg mass on a spring with k = 70 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.4 kgk = 70 N/mA = 4 cm
E = J
6.Hard
mk = 50 N/mA = 6 cmx = 2 cm

A mass on a spring with k = 50 N/m oscillates on a frictionless surface with an amplitude of 6 cm. Find the energy U stored in the spring when the mass is 2 cm from equilibrium.

k = 50 N/mA = 6 cmx = 2 cm
U = J

Answer key

  1. 1. f = 1.28 Hz
  2. 2. T = 0.6774 s
  3. 3. T = 1.099 s
  4. 4. v = −0.3038 m/s
  5. 5. E = 0.056 J
  6. 6. U = 0.01 J

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