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
2.2 kgk = ?23 cm

Hanging a 2.2 kg mass on a spring stretches it by 23 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 2.2 kgx = 23 cmg = 9.81 m/s²
k = N/m
2.Easy
4.8 kgk = 10 N/m

A 4.8 kg mass on a spring with stiffness 10 N/m oscillates on a frictionless surface. Find the period T.

m = 4.8 kgk = 10 N/m
T = s
3.Medium
L = ?

How long must a simple pendulum be to have a period of 1.4 s? Use g = 9.81 m/s². Find L.

T = 1.4 sg = 9.81 m/s²
L = m
4.Medium
t (s)x (cm)0.35 s

A 1.7 kg mass on a spring with k = 170 N/m is pulled 10 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 0.35 s (with sign).

m = 1.7 kgk = 170 N/mA = 10 cmt = 0.35 s
x = cm
5.Hard
3.2 kgk = 140 N/mA = 7 cm

A 3.2 kg mass on a spring with k = 140 N/m is pulled 7 cm from equilibrium and released. Find its maximum acceleration amax.

m = 3.2 kgk = 140 N/mA = 7 cm
amax = m/s²
6.Hard
0.6 kgk = 30 N/mA = 11 cm

A 0.6 kg mass on a spring with k = 30 N/m is pulled 11 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.6 kgk = 30 N/mA = 11 cm
vmax = m/s

Answer key

  1. 1. k = 93.83 N/m
  2. 2. T = 4.353 s
  3. 3. L = 0.487 m
  4. 4. x = −9.365 cm
  5. 5. amax = 3.063 m/s²
  6. 6. vmax = 0.7778 m/s

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