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
1.8 kgk = 210 N/m

A 1.8 kg mass on a spring with stiffness 210 N/m oscillates on a frictionless surface. Find the period T.

m = 1.8 kgk = 210 N/m
T = s
2.Easy
3.3 kgk = ?

A 3.3 kg mass on a spring oscillates with a period of 1.1 s. Find the spring stiffness k.

m = 3.3 kgT = 1.1 s
k = N/m
3.Medium
L = 2 mT = 2.66 s

An astronaut on another planet finds that a simple pendulum 2 m long has a period of 2.66 s for small swings. Find the gravitational acceleration g on that planet.

L = 2 mT = 2.66 s
g = m/s²
4.Medium
t (s)x (cm)0.3 s

A 3.7 kg mass on a spring with k = 170 N/m is pulled 4 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.3 s (with sign).

m = 3.7 kgk = 170 N/mA = 4 cmt = 0.3 s
x = cm
5.Hard
0.4 kgk = 290 N/m

A 0.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 290 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 0.4 kgk = 290 N/mg = 9.81 m/s²
xmax = cm
6.Hard
2.9 kgk = 250 N/m

A 2.9 kg mass is attached to the lower end of an unstretched vertical spring with k = 250 N/m and released from rest. Use g = 9.81 m/s². Find the greatest extension xmax of the spring in cm.

m = 2.9 kgk = 250 N/mg = 9.81 m/s²
xmax = cm

Answer key

  1. 1. T = 0.5817 s
  2. 2. k = 107.7 N/m
  3. 3. g = 11.16 m/s²
  4. 4. x = −1.785 cm
  5. 5. xmax = 2.706 cm
  6. 6. xmax = 22.76 cm

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