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
1.6 kgk = ?

A 1.6 kg mass on a spring oscillates with a period of 1.3 s. Find the spring stiffness k.

m = 1.6 kgT = 1.3 s
k = N/m
2.Easy
2.4 kgk = 290 N/m

A 2.4 kg mass on a spring with stiffness 290 N/m oscillates on a frictionless surface. Find the frequency f.

m = 2.4 kgk = 290 N/m
f = Hz
3.Medium
t (s)x (cm)0.05 s

A 3.5 kg mass on a spring with k = 350 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 = 0.05 s (with sign).

m = 3.5 kgk = 350 N/mA = 4 cmt = 0.05 s
x = cm
4.Medium
L = 1.3 mT = 1.44 s

An astronaut on another planet finds that a simple pendulum 1.3 m long has a period of 1.44 s for small swings. Find the gravitational acceleration g on that planet.

L = 1.3 mT = 1.44 s
g = m/s²
5.Hard
1.8 kgk = 400 N/mA = 7 cm

A 1.8 kg mass on a spring with k = 400 N/m is pulled 7 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.8 kgk = 400 N/mA = 7 cm
E = J
6.Hard
t (s)x (cm)t = ?2

A body oscillates in simple harmonic motion with period 3.4 s and amplitude 4 cm. What is the shortest time t it needs to move from its maximum displacement of 4 cm to a displacement of 2 cm?

T = 3.4 sA = 4 cmx = 2 cm
t = s

Answer key

  1. 1. k = 37.38 N/m
  2. 2. f = 1.749 Hz
  3. 3. x = 3.51 cm
  4. 4. g = 24.75 m/s²
  5. 5. E = 0.98 J
  6. 6. t = 0.5667 s

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