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.

New worksheetPractise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________   Date: ____________

1.Easy
3.7 kgk = 30 N/m

A 3.7 kg mass on a spring with stiffness 30 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.7 kgk = 30 N/m
f = Hz
2.Easy
2 kgk

A 2 kg mass on a spring makes 40 complete oscillations in 37 s. Find the frequency f of the oscillation.

m = 2 kgN = 40t = 37 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.8 s? Use g = 9.81 m/s². Find L.

T = 2.8 sg = 9.81 m/s²
L = m
4.Medium
L = 1.4 mT = 5.84 s

An astronaut on another planet finds that a simple pendulum 1.4 m long has a period of 5.84 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.4 mT = 5.84 s
g = m/s²
5.Hard
mk = 360 N/mA = 17 cmx = 1 cm

A mass on a spring with k = 360 N/m oscillates on a frictionless surface with an amplitude of 17 cm. Find the energy U stored in the spring when the mass is 1 cm from equilibrium.

k = 360 N/mA = 17 cmx = 1 cm
U = J
6.Hard
1.4 kgk = 320 N/m

A 1.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 320 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 1.4 kgk = 320 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. f = 0.4532 Hz
  2. 2. f = 1.081 Hz
  3. 3. L = 1.948 m
  4. 4. g = 1.621 m/s²
  5. 5. U = 0.018 J
  6. 6. xmax = 8.584 cm

Full step-by-step solutions: practise this topic on examproblems.com.