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
2.3 kgk = 200 N/m

A 2.3 kg mass on a spring with stiffness 200 N/m oscillates on a frictionless surface. Find the period T.

m = 2.3 kgk = 200 N/m
T = s
2.Easy
0.7 kgk

A 0.7 kg mass on a spring makes 50 complete oscillations in 39 s. Find the frequency f of the oscillation.

m = 0.7 kgN = 50t = 39 s
f = Hz
3.Medium
L = ?

How long must a simple pendulum be to have a period of 0.9 s? Use g = 9.81 m/s². Find L.

T = 0.9 sg = 9.81 m/s²
L = m
4.Medium
L = ?

How long must a simple pendulum be to have a period of 1.6 s? Use g = 9.81 m/s². Find L.

T = 1.6 sg = 9.81 m/s²
L = m
5.Hard
3.7 kgk = 30 N/mA = 13 cm

A 3.7 kg mass on a spring with k = 30 N/m is pulled 13 cm from equilibrium and released. Find its maximum speed vmax.

m = 3.7 kgk = 30 N/mA = 13 cm
vmax = m/s
6.Hard
t (s)x (cm)t = ?9.6

A body oscillates in simple harmonic motion with period 2.2 s and amplitude 16 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 9.6 cm?

T = 2.2 sA = 16 cmx = 9.6 cm
t = s

Answer key

  1. 1. T = 0.6738 s
  2. 2. f = 1.282 Hz
  3. 3. L = 0.2013 m
  4. 4. L = 0.6361 m
  5. 5. vmax = 0.3702 m/s
  6. 6. t = 0.2253 s

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