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 kgk = 330 N/m

A 1 kg mass on a spring with stiffness 330 N/m oscillates on a frictionless surface. Find the period T.

m = 1 kgk = 330 N/m
T = s
2.Easy
2.4 kgk

A 2.4 kg mass on a spring makes 40 complete oscillations in 40 s. Find the frequency f of the oscillation.

m = 2.4 kgN = 40t = 40 s
f = Hz
3.Medium
1.3 kgk = 490 N/mA = 13 cmx = 11 cm

A 1.3 kg mass on a spring with k = 490 N/m oscillates on a frictionless surface with an amplitude of 13 cm. Find its speed v when it is 11 cm from equilibrium.

m = 1.3 kgk = 490 N/mA = 13 cmx = 11 cm
v = m/s
4.Medium
t (s)x (cm)1.4 s

A 3.9 kg mass on a spring with k = 160 N/m is pulled 3 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.4 s (with sign).

m = 3.9 kgk = 160 N/mA = 3 cmt = 1.4 s
x = cm
5.Hard
3.4 kgk = 230 N/mA = 20 cm

A 3.4 kg mass on a spring with k = 230 N/m is pulled 20 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.4 kgk = 230 N/mA = 20 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?11.2

A body oscillates in simple harmonic motion with period 3.8 s and amplitude 14 cm. What is the shortest time t it needs to move from its maximum displacement of 14 cm to a displacement of 11.2 cm?

T = 3.8 sA = 14 cmx = 11.2 cm
t = s

Answer key

  1. 1. T = 0.3459 s
  2. 2. f = 1 Hz
  3. 3. v = 1.345 m/s
  4. 4. x = −2.691 cm
  5. 5. vmax = 1.645 m/s
  6. 6. t = 0.3892 s

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