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
3.5 kgk = ?

A 3.5 kg mass on a spring oscillates with a period of 0.75 s. Find the spring stiffness k.

m = 3.5 kgT = 0.75 s
k = N/m
2.Easy
3.8 kgk = ?

A 3.8 kg mass on a spring makes 20 complete oscillations in 41 s. Find the spring stiffness k.

m = 3.8 kgN = 20t = 41 s
k = N/m
3.Medium
t (s)x (cm)1 s

A 3.1 kg mass on a spring with k = 240 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1 s (with sign).

m = 3.1 kgk = 240 N/mA = 15 cmt = 1 s
x = cm
4.Medium
L = 0.4 m

A simple pendulum has a length of 0.4 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.4 mg = 9.81 m/s²
T = s
5.Hard
mk = 240 N/mA = 5 cmx = 4 cm

A mass on a spring with k = 240 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find the energy U stored in the spring when the mass is 4 cm from equilibrium.

k = 240 N/mA = 5 cmx = 4 cm
U = J
6.Hard
t (s)x (cm)t = ?3.6

A body oscillates in simple harmonic motion with period 2.1 s and amplitude 6 cm. What is the shortest time t it needs to move from its maximum displacement of 6 cm to a displacement of 3.6 cm?

T = 2.1 sA = 6 cmx = 3.6 cm
t = s

Answer key

  1. 1. k = 245.6 N/m
  2. 2. k = 35.7 N/m
  3. 3. x = −12.16 cm
  4. 4. T = 1.269 s
  5. 5. U = 0.192 J
  6. 6. t = 0.3099 s

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