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
0.7 kgk

A 0.7 kg mass on a spring makes 40 complete oscillations in 34 s. Find the frequency f of the oscillation.

m = 0.7 kgN = 40t = 34 s
f = Hz
2.Easy
1.8 kgk = 210 N/m

A 1.8 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.8 kgk = 210 N/m
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
t (s)x (cm)1.25 s

A 1.5 kg mass on a spring with k = 50 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.25 s (with sign).

m = 1.5 kgk = 50 N/mA = 13 cmt = 1.25 s
x = cm
5.Hard
mk = 460 N/mA = 14 cmx = 5 cm

A mass on a spring with k = 460 N/m oscillates on a frictionless surface with an amplitude of 14 cm. Find its kinetic energy K when it is 5 cm from equilibrium.

k = 460 N/mA = 14 cmx = 5 cm
K = J
6.Hard
2.8 kgk = 160 N/mA = 19 cm

A 2.8 kg mass on a spring with k = 160 N/m is pulled 19 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 2.8 kgk = 160 N/mA = 19 cm
E = J

Answer key

  1. 1. f = 1.176 Hz
  2. 2. f = 1.719 Hz
  3. 3. L = 1.948 m
  4. 4. x = 7.733 cm
  5. 5. K = 3.933 J
  6. 6. E = 2.888 J

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