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
1.9 kgk13.5 cm

Hanging a 1.9 kg mass on a spring stretches it by 13.5 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 = 1.9 kgx = 13.5 cmg = 9.81 m/s²
T = s
2.Easy
0.6 kgk19.5 cm

Hanging a 0.6 kg mass on a spring stretches it by 19.5 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 = 0.6 kgx = 19.5 cmg = 9.81 m/s²
T = s
3.Medium
L = 1.7 mT = 6.44 s

An astronaut on another planet finds that a simple pendulum 1.7 m long has a period of 6.44 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.7 mT = 6.44 s
g = m/s²
4.Medium
L = ?

How long must a simple pendulum be to have a period of 2.6 s? Use g = 9.81 m/s². Find L.

T = 2.6 sg = 9.81 m/s²
L = m
5.Hard
3.3 kgk = 370 N/mA = 9 cm

A 3.3 kg mass on a spring with k = 370 N/m is pulled 9 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.3 kgk = 370 N/mA = 9 cm
E = J
6.Hard
t (s)x (cm)t = ?6.6

A body oscillates in simple harmonic motion with period 0.5 s and amplitude 11 cm. What is the shortest time t it needs to move from its maximum displacement of 11 cm to a displacement of 6.6 cm?

T = 0.5 sA = 11 cmx = 6.6 cm
t = s

Answer key

  1. 1. T = 0.7371 s
  2. 2. T = 0.8859 s
  3. 3. g = 1.618 m/s²
  4. 4. L = 1.68 m
  5. 5. E = 1.498 J
  6. 6. t = 0.07379 s

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