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 kgk = 310 N/m

A 4 kg mass on a spring with stiffness 310 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4 kgk = 310 N/m
f = Hz
2.Easy
0.3 kgk = 400 N/m

A 0.3 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.3 kgk = 400 N/m
f = Hz
3.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
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
5.Hard
mk = 300 N/mA = 15 cmx = 6 cm

A mass on a spring with k = 300 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 6 cm from equilibrium.

k = 300 N/mA = 15 cmx = 6 cm
U = J
6.Hard
3 kgk = 490 N/mA = 5 cm

A 3 kg mass on a spring with k = 490 N/m is pulled 5 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3 kgk = 490 N/mA = 5 cm
amax = m/s²

Answer key

  1. 1. f = 1.401 Hz
  2. 2. f = 5.812 Hz
  3. 3. L = 0.8051 m
  4. 4. L = 1.948 m
  5. 5. U = 0.54 J
  6. 6. amax = 8.167 m/s²

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