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
0.5 kgk = ?

A 0.5 kg mass on a spring makes 30 complete oscillations in 24 s. Find the spring stiffness k.

m = 0.5 kgN = 30t = 24 s
k = N/m
2.Easy
0.5 kgk1 cm

Hanging a 0.5 kg mass on a spring stretches it by 1 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.5 kgx = 1 cmg = 9.81 m/s²
T = s
3.Medium
t (s)x (cm)0.7 s

A 2.6 kg mass on a spring with k = 90 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.7 s (with sign).

m = 2.6 kgk = 90 N/mA = 3 cmt = 0.7 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.4 s? Use g = 9.81 m/s². Find L.

T = 2.4 sg = 9.81 m/s²
L = m
5.Hard
3.6 kgk = 300 N/mA = 11 cm

A 3.6 kg mass on a spring with k = 300 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.6 kgk = 300 N/mA = 11 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?4

A body oscillates in simple harmonic motion with period 2.9 s and amplitude 8 cm. What is the shortest time t it needs to move from its maximum displacement of 8 cm to a displacement of 4 cm?

T = 2.9 sA = 8 cmx = 4 cm
t = s

Answer key

  1. 1. k = 30.84 N/m
  2. 2. T = 0.2006 s
  3. 3. x = −1.679 cm
  4. 4. L = 1.431 m
  5. 5. vmax = 1.004 m/s
  6. 6. t = 0.4833 s

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