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
4.5 kgk = 30 N/m

A 4.5 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.5 kgk = 30 N/m
f = Hz
2.Easy
4.7 kgk = 320 N/m

A 4.7 kg mass on a spring with stiffness 320 N/m oscillates on a frictionless surface. Find the period T.

m = 4.7 kgk = 320 N/m
T = s
3.Medium
L = 1.9 mT = 6.8 s

An astronaut on another planet finds that a simple pendulum 1.9 m long has a period of 6.8 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.9 mT = 6.8 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
5.Hard
0.2 kgk = 250 N/mA = 10 cm

A 0.2 kg mass on a spring with k = 250 N/m is pulled 10 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.2 kgk = 250 N/mA = 10 cm
amax = m/s²
6.Hard
mk = 50 N/mA = 13 cmx = 9 cm

A mass on a spring with k = 50 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its kinetic energy K when it is 9 cm from equilibrium.

k = 50 N/mA = 13 cmx = 9 cm
K = J

Answer key

  1. 1. f = 0.4109 Hz
  2. 2. T = 0.7615 s
  3. 3. g = 1.622 m/s²
  4. 4. L = 0.6361 m
  5. 5. amax = 125 m/s²
  6. 6. K = 0.22 J

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