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
0.8 kgk = ?

A 0.8 kg mass on a spring oscillates with a period of 0.55 s. Find the spring stiffness k.

m = 0.8 kgT = 0.55 s
k = N/m
2.Easy
2.9 kgk = 60 N/m

A 2.9 kg mass on a spring with stiffness 60 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.9 kgk = 60 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
4.Medium
L = 0.6 mT = 3.82 s

An astronaut on another planet finds that a simple pendulum 0.6 m long has a period of 3.82 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.6 mT = 3.82 s
g = m/s²
5.Hard
mk = 130 N/mA = 11 cmx = 2 cm

A mass on a spring with k = 130 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its kinetic energy K when it is 2 cm from equilibrium.

k = 130 N/mA = 11 cmx = 2 cm
K = J
6.Hard
3 kgk = 390 N/m

A 3 kg mass is attached to the lower end of an unstretched vertical spring with k = 390 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 3 kgk = 390 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. k = 104.4 N/m
  2. 2. f = 0.7239 Hz
  3. 3. L = 1.68 m
  4. 4. g = 1.623 m/s²
  5. 5. K = 0.7605 J
  6. 6. xmax = 15.09 cm

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