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
0.4 kgk = 400 N/m

A 0.4 kg mass on a spring with stiffness 400 N/m oscillates on a frictionless surface. Find the frequency f.

m = 0.4 kgk = 400 N/m
f = Hz
2.Easy
3.4 kgk = ?

A 3.4 kg mass on a spring oscillates with a period of 1.8 s. Find the spring stiffness k.

m = 3.4 kgT = 1.8 s
k = N/m
3.Medium
2.4 kgk = 440 N/mA = 11 cmx = 8 cm

A 2.4 kg mass on a spring with k = 440 N/m oscillates on a frictionless surface with an amplitude of 11 cm. Find its speed v when it is 8 cm from equilibrium.

m = 2.4 kgk = 440 N/mA = 11 cmx = 8 cm
v = m/s
4.Medium
t (s)x (cm)0.65 s

A 2.8 kg mass on a spring with k = 180 N/m is pulled 6 cm in the positive direction and released from rest at t = 0. Find its velocity v at t = 0.65 s (with sign).

m = 2.8 kgk = 180 N/mA = 6 cmt = 0.65 s
v = m/s
5.Hard
1.3 kgk = 360 N/mA = 13 cm

A 1.3 kg mass on a spring with k = 360 N/m is pulled 13 cm from equilibrium and released. Find the total energy E of the oscillation.

m = 1.3 kgk = 360 N/mA = 13 cm
E = J
6.Hard
t (s)x (cm)t = ?10.4

A body oscillates in simple harmonic motion with period 3.7 s and amplitude 13 cm. What is the shortest time t it needs to move from equilibrium to a displacement of 10.4 cm?

T = 3.7 sA = 13 cmx = 10.4 cm
t = s

Answer key

  1. 1. f = 5.033 Hz
  2. 2. k = 41.43 N/m
  3. 3. v = 1.022 m/s
  4. 4. v = 0.4224 m/s
  5. 5. E = 3.042 J
  6. 6. t = 0.5461 s

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