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 = 260 N/m

A 4.1 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the period T.

m = 4.1 kgk = 260 N/m
T = s
2.Easy
0.2 kgk = ?

A 0.2 kg mass on a spring oscillates with a period of 0.6 s. Find the spring stiffness k.

m = 0.2 kgT = 0.6 s
k = N/m
3.Medium
t (s)x (cm)0.25 s

A 3.7 kg mass on a spring with k = 240 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 = 0.25 s (with sign).

m = 3.7 kgk = 240 N/mA = 4 cmt = 0.25 s
x = cm
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.1 s? Use g = 9.81 m/s². Find L.

T = 1.1 sg = 9.81 m/s²
L = m
5.Hard
1.9 kgk = 340 N/mA = 6 cm

A 1.9 kg mass on a spring with k = 340 N/m is pulled 6 cm from equilibrium and released. Find its maximum acceleration amax.

m = 1.9 kgk = 340 N/mA = 6 cm
amax = m/s²
6.Hard
3 kgk = 40 N/mA = 2 cm

A 3 kg mass on a spring with k = 40 N/m is pulled 2 cm from equilibrium and released. Find its maximum speed vmax.

m = 3 kgk = 40 N/mA = 2 cm
vmax = m/s

Answer key

  1. 1. T = 0.789 s
  2. 2. k = 21.93 N/m
  3. 3. x = −1.713 cm
  4. 4. L = 0.3007 m
  5. 5. amax = 10.74 m/s²
  6. 6. vmax = 0.07303 m/s

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