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
1.7 kgk = 220 N/m

A 1.7 kg mass on a spring with stiffness 220 N/m oscillates on a frictionless surface. Find the frequency f.

m = 1.7 kgk = 220 N/m
f = Hz
2.Easy
0.6 kgk24.5 cm

Hanging a 0.6 kg mass on a spring stretches it by 24.5 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 = 0.6 kgx = 24.5 cmg = 9.81 m/s²
T = s
3.Medium
L = 0.3 m

A simple pendulum has a length of 0.3 m. Use g = 9.81 m/s². Find its period T for small swings.

L = 0.3 mg = 9.81 m/s²
T = s
4.Medium
t (s)x (cm)0.45 s

A 1.5 kg mass on a spring with k = 40 N/m is pulled 15 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.45 s (with sign).

m = 1.5 kgk = 40 N/mA = 15 cmt = 0.45 s
v = m/s
5.Hard
t (s)x (cm)t = ?6

A body oscillates in simple harmonic motion with period 3.9 s and amplitude 8 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 6 cm?

T = 3.9 sA = 8 cmx = 6 cm
t = s
6.Hard
2 kgk = 1100 N/m400 m/s

A 20 g bullet moving at 400 m/s hits and stays in a 2 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 1100 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 20 gv = 400 m/sM = 2 kgk = 1100 N/m
A = cm

Answer key

  1. 1. f = 1.811 Hz
  2. 2. T = 0.993 s
  3. 3. T = 1.099 s
  4. 4. v = −0.5652 m/s
  5. 5. t = 0.5264 s
  6. 6. A = 16.97 cm

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