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 kgk = 120 N/m

A 3 kg mass on a spring with stiffness 120 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3 kgk = 120 N/m
f = Hz
2.Easy
1 kgk = ?

A 1 kg mass on a spring makes 15 complete oscillations in 35 s. Find the spring stiffness k.

m = 1 kgN = 15t = 35 s
k = N/m
3.Medium
L = ?

How long must a simple pendulum be to have a period of 2.1 s? Use g = 9.81 m/s². Find L.

T = 2.1 sg = 9.81 m/s²
L = m
4.Medium
3.2 kgk = 410 N/mA = 5 cmx = 1 cm

A 3.2 kg mass on a spring with k = 410 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 = 3.2 kgk = 410 N/mA = 5 cmx = 1 cm
v = m/s
5.Hard
t (s)x (cm)t = ?4

A body oscillates in simple harmonic motion with period 2.8 s and amplitude 16 cm. What is the shortest time t it needs to move from its maximum displacement of 16 cm to a displacement of 4 cm?

T = 2.8 sA = 16 cmx = 4 cm
t = s
6.Hard
3.9 kgk = 280 N/mA = 12 cm

A 3.9 kg mass on a spring with k = 280 N/m is pulled 12 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 3.9 kgk = 280 N/mA = 12 cm
E = J

Answer key

  1. 1. f = 1.007 Hz
  2. 2. k = 7.251 N/m
  3. 3. L = 1.096 m
  4. 4. v = 0.5545 m/s
  5. 5. t = 0.5874 s
  6. 6. E = 2.016 J

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