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
1.1 kgk = ?

A 1.1 kg mass on a spring makes 50 complete oscillations in 28 s. Find the spring stiffness k.

m = 1.1 kgN = 50t = 28 s
k = N/m
2.Easy
1.9 kgk = 280 N/m

A 1.9 kg mass on a spring with stiffness 280 N/m oscillates on a frictionless surface. Find the period T.

m = 1.9 kgk = 280 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
4.Medium
3.1 kgk = 30 N/mA = 4 cmx = 1 cm

A 3.1 kg mass on a spring with k = 30 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 1 cm from equilibrium.

m = 3.1 kgk = 30 N/mA = 4 cmx = 1 cm
v = m/s
5.Hard
0.3 kgk = 180 N/m

A 0.3 kg mass is attached to the lower end of an unstretched vertical spring with k = 180 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.3 kgk = 180 N/mg = 9.81 m/s²
vmax = m/s
6.Hard
t (s)x (cm)t = ?1.5

A body oscillates in simple harmonic motion with period 2.9 s and amplitude 5 cm. What is the shortest time t it needs to move from its maximum displacement of 5 cm to a displacement of 1.5 cm?

T = 2.9 sA = 5 cmx = 1.5 cm
t = s

Answer key

  1. 1. k = 138.5 N/m
  2. 2. T = 0.5176 s
  3. 3. L = 1.68 m
  4. 4. v = 0.1205 m/s
  5. 5. vmax = 0.4005 m/s
  6. 6. t = 0.5844 s

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