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
4.7 kgk = 230 N/m

A 4.7 kg mass on a spring with stiffness 230 N/m oscillates on a frictionless surface. Find the frequency f.

m = 4.7 kgk = 230 N/m
f = Hz
2.Easy
0.4 kgk = 180 N/m

A 0.4 kg mass on a spring with stiffness 180 N/m oscillates on a frictionless surface. Find the period T.

m = 0.4 kgk = 180 N/m
T = s
3.Medium
L = 0.6 mT = 2.53 s

An astronaut on another planet finds that a simple pendulum 0.6 m long has a period of 2.53 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.6 mT = 2.53 s
g = m/s²
4.Medium
L = 0.9 mT = 3.09 s

An astronaut on another planet finds that a simple pendulum 0.9 m long has a period of 3.09 s for small swings. Find the gravitational acceleration g on that planet.

L = 0.9 mT = 3.09 s
g = m/s²
5.Hard
t (s)x (cm)t = ?4.8

A body oscillates in simple harmonic motion with period 3.7 s and amplitude 16 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.8 cm?

T = 3.7 sA = 16 cmx = 4.8 cm
t = s
6.Hard
1.5 kgk = 410 N/mA = 11 cm

A 1.5 kg mass on a spring with k = 410 N/m is pulled 11 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.5 kgk = 410 N/mA = 11 cm
E = J

Answer key

  1. 1. f = 1.113 Hz
  2. 2. T = 0.2962 s
  3. 3. g = 3.701 m/s²
  4. 4. g = 3.721 m/s²
  5. 5. t = 0.1794 s
  6. 6. E = 2.481 J

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