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
1.7 kgk = 70 N/m

A 1.7 kg mass on a spring with stiffness 70 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.7 kgk = 70 N/m
f = Hz
2.Easy
1.4 kgk = 220 N/m

A 1.4 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.4 kgk = 220 N/m
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.8 s? Use g = 9.81 m/s². Find L.

T = 0.8 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.4 s? Use g = 9.81 m/s². Find L.

T = 1.4 sg = 9.81 m/s²
L = m
5.Hard
3.5 kgk = 330 N/mA = 4 cm

A 3.5 kg mass on a spring with k = 330 N/m is pulled 4 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.5 kgk = 330 N/mA = 4 cm
amax = m/s²
6.Hard
0.1 kgk = 180 N/m

A 0.1 kg mass is attached to the lower end of an unstretched vertical spring with k = 180 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.1 kgk = 180 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. f = 1.021 Hz
  2. 2. f = 1.995 Hz
  3. 3. L = 0.159 m
  4. 4. L = 0.487 m
  5. 5. amax = 3.771 m/s²
  6. 6. xmax = 1.09 cm

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