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
0.5 kgk = 170 N/m

A 0.5 kg mass on a spring with stiffness 170 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.5 kgk = 170 N/m
f = Hz
2.Easy
3.2 kgk = ?

A 3.2 kg mass on a spring oscillates with a period of 1.55 s. Find the spring stiffness k.

m = 3.2 kgT = 1.55 s
k = N/m
3.Medium
t (s)x (cm)0.95 s

A 1.9 kg mass on a spring with k = 260 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 = 0.95 s (with sign).

m = 1.9 kgk = 260 N/mA = 4 cmt = 0.95 s
x = cm
4.Medium
L = 1.1 mT = 1.32 s

An astronaut on another planet finds that a simple pendulum 1.1 m long has a period of 1.32 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.1 mT = 1.32 s
g = m/s²
5.Hard
0.9 kgk = 460 N/mA = 14 cm

A 0.9 kg mass on a spring with k = 460 N/m is pulled 14 cm from equilibrium and released. Find its maximum acceleration amax.

m = 0.9 kgk = 460 N/mA = 14 cm
amax = m/s²
6.Hard
0.4 kgk = 150 N/mA = 20 cm

A 0.4 kg mass on a spring with k = 150 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 0.4 kgk = 150 N/mA = 20 cm
vmax = m/s

Answer key

  1. 1. f = 2.935 Hz
  2. 2. k = 52.58 N/m
  3. 3. x = 0.4688 cm
  4. 4. g = 24.92 m/s²
  5. 5. amax = 71.56 m/s²
  6. 6. vmax = 3.873 m/s

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