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
1.8 kgk = 390 N/m

A 1.8 kg mass on a spring with stiffness 390 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.8 kgk = 390 N/m
f = Hz
2.Easy
2.7 kgk = ?23.5 cm

Hanging a 2.7 kg mass on a spring stretches it by 23.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.7 kgx = 23.5 cmg = 9.81 m/s²
k = N/m
3.Medium
2.6 kgk = 440 N/mA = 12 cmx = 1 cm

A 2.6 kg mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 12 cm. Find its speed v when it is 1 cm from equilibrium.

m = 2.6 kgk = 440 N/mA = 12 cmx = 1 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.8 s? Use g = 9.81 m/s². Find L.

T = 1.8 sg = 9.81 m/s²
L = m
5.Hard
3 kgk = 300 N/m

A 3 kg mass is attached to the lower end of an unstretched vertical spring with k = 300 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 3 kgk = 300 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
mk = 320 N/mA = 19 cmx = 17 cm

A mass on a spring with k = 320 N/m oscillates on a frictionless surface with an amplitude of 19 cm. Find the energy U stored in the spring when the mass is 17 cm from equilibrium.

k = 320 N/mA = 19 cmx = 17 cm
U = J

Answer key

  1. 1. f = 2.343 Hz
  2. 2. k = 112.7 N/m
  3. 3. v = 1.556 m/s
  4. 4. L = 0.8051 m
  5. 5. vmax = 0.981 m/s
  6. 6. U = 4.624 J

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