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
1.3 kgk = 370 N/m

A 1.3 kg mass on a spring with stiffness 370 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.3 kgk = 370 N/m
f = Hz
2.Easy
2.8 kgk = 220 N/m

A 2.8 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.8 kgk = 220 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.3 s? Use g = 9.81 m/s². Find L.

T = 1.3 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1 s? Use g = 9.81 m/s². Find L.

T = 1 sg = 9.81 m/s²
L = m
5.Hard
0.8 kgk = 130 N/mA = 4 cm

A 0.8 kg mass on a spring with k = 130 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.8 kgk = 130 N/mA = 4 cm
vmax = m/s
6.Hard
mk = 60 N/mA = 19 cmx = 8 cm

A mass on a spring with k = 60 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find the energy U stored in the spring when the mass is 8 cm from equilibrium.

k = 60 N/mA = 19 cmx = 8 cm
U = J

Answer key

  1. 1. f = 2.685 Hz
  2. 2. f = 1.411 Hz
  3. 3. L = 0.4199 m
  4. 4. L = 0.2485 m
  5. 5. vmax = 0.5099 m/s
  6. 6. U = 0.192 J

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