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
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 2.05 s. Find the spring stiffness k.

m = 0.2 kgT = 2.05 s
k = N/m
2.Easy
0.7 kgk = 190 N/m

A 0.7 kg mass on a spring with stiffness 190 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 190 N/m
T = s
3.Medium
3.9 kgk = 250 N/mA = 20 cmx = 15 cm

A 3.9 kg mass on a spring with k = 250 N/m oscillates on a frictionless surface with an amplitude of 20 cm. Find its speed v when it is 15 cm from equilibrium.

m = 3.9 kgk = 250 N/mA = 20 cmx = 15 cm
v = m/s
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.5 s? Use g = 9.81 m/s². Find L.

T = 1.5 sg = 9.81 m/s²
L = m
5.Hard
0.4 kgk = 70 N/m

A 0.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 70 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.4 kgk = 70 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
1 kgk = 460 N/mA = 3 cm

A 1 kg mass on a spring with k = 460 N/m is pulled 3 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1 kgk = 460 N/mA = 3 cm
E = J

Answer key

  1. 1. k = 1.879 N/m
  2. 2. T = 0.3814 s
  3. 3. v = 1.059 m/s
  4. 4. L = 0.5591 m
  5. 5. vmax = 0.7416 m/s
  6. 6. E = 0.207 J

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