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
3.8 kgk = 100 N/m

A 3.8 kg mass on a spring with stiffness 100 N/m oscillates on a frictionless surface. Find the frequency f.

m = 3.8 kgk = 100 N/m
f = Hz
2.Easy
0.7 kgk = 340 N/m

A 0.7 kg mass on a spring with stiffness 340 N/m oscillates on a frictionless surface. Find the period T.

m = 0.7 kgk = 340 N/m
T = s
3.Medium
3.2 kgk = 290 N/mA = 4 cmx = 3 cm

A 3.2 kg mass on a spring with k = 290 N/m oscillates on a frictionless surface with an amplitude of 4 cm. Find its speed v when it is 3 cm from equilibrium.

m = 3.2 kgk = 290 N/mA = 4 cmx = 3 cm
v = m/s
4.Medium
1.7 kgk = 30 N/mA = 16 cmx = 10 cm

A 1.7 kg mass on a spring with k = 30 N/m oscillates on a frictionless surface with an amplitude of 16 cm. Find its speed v when it is 10 cm from equilibrium.

m = 1.7 kgk = 30 N/mA = 16 cmx = 10 cm
v = m/s
5.Hard
t (s)x (cm)t = ?9

A body oscillates in simple harmonic motion with period 1 s and amplitude 15 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 9 cm?

T = 1 sA = 15 cmx = 9 cm
t = s
6.Hard
t (s)x (cm)t = ?12

A body oscillates in simple harmonic motion with period 1.8 s and amplitude 15 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 12 cm?

T = 1.8 sA = 15 cmx = 12 cm
t = s

Answer key

  1. 1. f = 0.8164 Hz
  2. 2. T = 0.2851 s
  3. 3. v = 0.2519 m/s
  4. 4. v = 0.5247 m/s
  5. 5. t = 0.1024 s
  6. 6. t = 0.2657 s

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