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
2.1 kgk6.5 cm

Hanging a 2.1 kg mass on a spring stretches it by 6.5 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 = 2.1 kgx = 6.5 cmg = 9.81 m/s²
T = s
2.Easy
3.2 kgk

A 3.2 kg mass on a spring makes 10 complete oscillations in 8 s. Find the frequency f of the oscillation.

m = 3.2 kgN = 10t = 8 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.3 s? Use g = 9.81 m/s². Find L.

T = 1.3 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)1.5 s

A 0.5 kg mass on a spring with k = 250 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.5 s (with sign).

m = 0.5 kgk = 250 N/mA = 14 cmt = 1.5 s
x = cm
5.Hard
0.9 kgk = 320 N/mA = 20 cm

A 0.9 kg mass on a spring with k = 320 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.9 kgk = 320 N/mA = 20 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?9

A body oscillates in simple harmonic motion with period 3.7 s and amplitude 18 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 9 cm?

T = 3.7 sA = 18 cmx = 9 cm
t = s

Answer key

  1. 1. T = 0.5114 s
  2. 2. f = 1.25 Hz
  3. 3. L = 0.4199 m
  4. 4. x = −7.369 cm
  5. 5. vmax = 3.771 m/s
  6. 6. t = 0.3083 s

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