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
3.8 kgk = 190 N/m

A 3.8 kg mass on a spring with stiffness 190 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.8 kgk = 190 N/m
f = Hz
2.Easy
4.8 kgk = 40 N/m

A 4.8 kg mass on a spring with stiffness 40 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 40 N/m
T = s
3.Medium
1.5 kgk = 80 N/mA = 5 cmx = 2 cm

A 1.5 kg mass on a spring with k = 80 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 2 cm from equilibrium.

m = 1.5 kgk = 80 N/mA = 5 cmx = 2 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
5.Hard
2.9 kgk = 130 N/m

A 2.9 kg mass is attached to the lower end of an unstretched vertical spring with k = 130 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.9 kgk = 130 N/mg = 9.81 m/s²
xmax = cm
6.Hard
1.2 kgk = 170 N/mA = 7 cm

A 1.2 kg mass on a spring with k = 170 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.2 kgk = 170 N/mA = 7 cm
amax = m/s²

Answer key

  1. 1. f = 1.125 Hz
  2. 2. T = 2.177 s
  3. 3. v = 0.3347 m/s
  4. 4. L = 1.431 m
  5. 5. xmax = 43.77 cm
  6. 6. amax = 9.917 m/s²

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