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 = ?15 cm

Hanging a 2.2 kg mass on a spring stretches it by 15 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.2 kgx = 15 cmg = 9.81 m/s²
k = N/m
2.Easy
3.9 kgk = 90 N/m

A 3.9 kg mass on a spring with stiffness 90 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.9 kgk = 90 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 3 s? Use g = 9.81 m/s². Find L.

T = 3 sg = 9.81 m/s²
L = m
4.Medium
L = 1.2 m

A simple pendulum has a length of 1.2 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 1.2 mg = 9.81 m/s²
T = s
5.Hard
2.3 kgk = 350 N/mA = 17 cm

A 2.3 kg mass on a spring with k = 350 N/m is pulled 17 cm from equilibrium and released. Find its maximum acceleration amax.

m = 2.3 kgk = 350 N/mA = 17 cm
amax = m/s²
6.Hard
mk = 220 N/mA = 15 cmx = 7 cm

A mass on a spring with k = 220 N/m oscillates on a frictionless surface with an amplitude of 15 cm. Find the energy U stored in the spring when the mass is 7 cm from equilibrium.

k = 220 N/mA = 15 cmx = 7 cm
U = J

Answer key

  1. 1. k = 143.9 N/m
  2. 2. f = 0.7646 Hz
  3. 3. L = 2.236 m
  4. 4. T = 2.198 s
  5. 5. amax = 25.87 m/s²
  6. 6. U = 0.539 J

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