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
3.6 kgk = 260 N/m

A 3.6 kg mass on a spring with stiffness 260 N/m oscillates on a frictionless surface. Find the period T.

m = 3.6 kgk = 260 N/m
T = s
2.Easy
3.6 kgk = ?

A 3.6 kg mass on a spring makes 40 complete oscillations in 45 s. Find the spring stiffness k.

m = 3.6 kgN = 40t = 45 s
k = N/m
3.Medium
t (s)x (cm)1.3 s

A 2 kg mass on a spring with k = 120 N/m is pulled 13 cm in the positive direction and released from rest at t = 0. Find its displacement x from equilibrium at t = 1.3 s (with sign).

m = 2 kgk = 120 N/mA = 13 cmt = 1.3 s
x = cm
4.Medium
0.4 kgk = 290 N/mA = 5 cmx = 1 cm

A 0.4 kg mass on a spring with k = 290 N/m oscillates on a frictionless surface with an amplitude of 5 cm. Find its speed v when it is 1 cm from equilibrium.

m = 0.4 kgk = 290 N/mA = 5 cmx = 1 cm
v = m/s
5.Hard
t (s)x (cm)t = ?4.2

A body oscillates in simple harmonic motion with period 3.3 s and amplitude 6 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 4.2 cm?

T = 3.3 sA = 6 cmx = 4.2 cm
t = s
6.Hard
0.4 kgk = 130 N/m

A 0.4 kg mass is attached to the lower end of an unstretched vertical spring with k = 130 N/m and released from rest. Use g = 9.81 m/s². Find the greatest speed vmax of the mass.

m = 0.4 kgk = 130 N/mg = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. T = 0.7393 s
  2. 2. k = 112.3 N/m
  3. 3. x = −10.39 cm
  4. 4. v = 1.319 m/s
  5. 5. t = 0.4072 s
  6. 6. vmax = 0.5442 m/s

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