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 = ?24 cm

Hanging a 1.8 kg mass on a spring stretches it by 24 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.8 kgx = 24 cmg = 9.81 m/s²
k = N/m
2.Easy
4.9 kgk = 300 N/m

A 4.9 kg mass on a spring with stiffness 300 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.9 kgk = 300 N/m
f = Hz
3.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
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.1 s? Use g = 9.81 m/s². Find L.

T = 1.1 sg = 9.81 m/s²
L = m
5.Hard
t (s)x (cm)t = ?10.8

A body oscillates in simple harmonic motion with period 2.3 s and amplitude 12 cm. What is the shortest time t it needs to move from its maximum displacement of 12 cm to a displacement of 10.8 cm?

T = 2.3 sA = 12 cmx = 10.8 cm
t = s
6.Hard
0.6 kgk = 220 N/m

A 0.6 kg mass is attached to the lower end of an unstretched vertical spring with k = 220 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.6 kgk = 220 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. k = 73.58 N/m
  2. 2. f = 1.245 Hz
  3. 3. L = 1.431 m
  4. 4. L = 0.3007 m
  5. 5. t = 0.1651 s
  6. 6. xmax = 5.351 cm

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