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.

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1.Easy
2.1 kgk

A 2.1 kg mass on a spring makes 30 complete oscillations in 50 s. Find the frequency f of the oscillation.

m = 2.1 kgN = 30t = 50 s
f = Hz
2.Easy
1.6 kgk = ?19.5 cm

Hanging a 1.6 kg mass on a spring stretches it by 19.5 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.6 kgx = 19.5 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1 mT = 4.94 s

An astronaut on another planet finds that a simple pendulum 1 m long has a period of 4.94 s for small swings. Find the gravitational acceleration g on that planet.

L = 1 mT = 4.94 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.2 s? Use g = 9.81 m/s². Find L.

T = 2.2 sg = 9.81 m/s²
L = m
5.Hard
0.2 kgk = 310 N/m

A 0.2 kg mass is attached to the lower end of an unstretched vertical spring with k = 310 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.2 kgk = 310 N/mg = 9.81 m/s²
xmax = cm
6.Hard
0.3 kgk = 430 N/mA = 6 cm

A 0.3 kg mass on a spring with k = 430 N/m is pulled 6 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.3 kgk = 430 N/mA = 6 cm
E = J

Answer key

  1. 1. f = 0.6 Hz
  2. 2. k = 80.49 N/m
  3. 3. g = 1.618 m/s²
  4. 4. L = 1.203 m
  5. 5. xmax = 1.266 cm
  6. 6. E = 0.774 J

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