Question

A block is attached to a spring and executes

simple harmonic motion according to x = 2.0
cos(50t), where x is in meters and t is in
seconds. The spring constant is k = 100 N/m.
What is the mass of the block?

Answer 1

.04 kg

Step-by-step explanation:

The equation for simple harmonic motion is x = A*cos(ωt), where A is the amplitude, ω is the angular frequency, and t is the time.

Comparing the given equation x = 2.0cos(50t) with the equation for simple harmonic motion, we see that A = 2.0 meters and ω = 50 radians/second.

The angular frequency is related to the spring constant and mass by the equation ω = sqrt(k/m), where sqrt denotes the square root.

Substituting the values given, we get:

50 = sqrt(100/m)

Squaring both sides and solving for m, we get:

m = 100/2500 = 0.04 kg