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
4.1 kgk = ?

A 4.1 kg mass on a spring oscillates with a period of 2.3 s. Find the spring stiffness k.

m = 4.1 kgT = 2.3 s
k = N/m
2.Easy
1.4 kgk = 150 N/m

A 1.4 kg mass on a spring with stiffness 150 N/m oscillates on a frictionless surface. Find the period T.

m = 1.4 kgk = 150 N/m
T = s
3.Medium
L = 1.7 mT = 4.25 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 4.25 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 4.25 s
g = m/s²
4.Medium
t (s)x (cm)1.05 s

A 2 kg mass on a spring with k = 150 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.05 s (with sign).

m = 2 kgk = 150 N/mA = 6 cmt = 1.05 s
x = cm
5.Hard
0.3 kgk = 350 N/mA = 4 cm

A 0.3 kg mass on a spring with k = 350 N/m is pulled 4 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 0.3 kgk = 350 N/mA = 4 cm
E = J
6.Hard
0.4 kgk = 170 N/mA = 4 cm

A 0.4 kg mass on a spring with k = 170 N/m is pulled 4 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.4 kgk = 170 N/mA = 4 cm
vmax = m/s

Answer key

  1. 1. k = 30.6 N/m
  2. 2. T = 0.607 s
  3. 3. g = 3.716 m/s²
  4. 4. x = −5.673 cm
  5. 5. E = 0.28 J
  6. 6. vmax = 0.8246 m/s

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