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
0.3 kgk20 cm

Hanging a 0.3 kg mass on a spring stretches it by 20 cm. Use g = 9.81 m/s². The mass is then pulled down a little and released. Find the period T of its oscillation.

m = 0.3 kgx = 20 cmg = 9.81 m/s²
T = s
2.Easy
1.1 kgk = ?4 cm

Hanging a 1.1 kg mass on a spring stretches it by 4 cm. Use g = 9.81 m/s². Find the stiffness k of the spring.

m = 1.1 kgx = 4 cmg = 9.81 m/s²
k = N/m
3.Medium
L = 1.7 mT = 2.45 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 2.45 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 2.45 s
g = m/s²
4.Medium
t (s)x (cm)1.15 s

A 1.1 kg mass on a spring with k = 240 N/m is pulled 14 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 1.15 s (with sign).

m = 1.1 kgk = 240 N/mA = 14 cmt = 1.15 s
v = m/s
5.Hard
0.5 kgk = 900 N/m100 m/s

A 12 g bullet moving at 100 m/s hits and stays in a 0.5 kg block resting on a frictionless surface. The block is attached to a horizontal spring with k = 900 N/m. Find the amplitude A of the resulting oscillation in cm.

m = 12 gv = 100 m/sM = 0.5 kgk = 900 N/m
A = cm
6.Hard
3.2 kgk = 270 N/mA = 12 cm

A 3.2 kg mass on a spring with k = 270 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.2 kgk = 270 N/mA = 12 cm
E = J

Answer key

  1. 1. T = 0.8971 s
  2. 2. k = 269.8 N/m
  3. 3. g = 11.18 m/s²
  4. 4. v = 1.98 m/s
  5. 5. A = 5.59 cm
  6. 6. E = 1.944 J

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