The force applied on the mass by the spring is determined as 6,252.96 N.
How to calculate the force of the spring?
The force of the spring is calculated by applying Hooke's law as follows.
F = kx
where;
- k is the spring constant
- x is the extension of the spring.
The angular speed of the spring is;
ω = 2π/T
ω = 2πf
ω = 2π x 20 Hz
ω = 125.66 rad/s
The spring constant of the spring is calculated as follows;
ω = √ (k/m)
where;
- m is the mass
- k is the spring constant
ω² = k/m
k = ω²m
k = (125.66²) x 0.33 kg
k = 5,210.8 N/m
The general displacement equation of waves is;
x(t) = A cos(ωt)
After 3.3 seconds;
x(3.3) = 1.2 m cos(125.66 x 3.3)
x(3.3) = 1.2 m x 0.9999
x(3.3) = 1.2 m
The force applied on the mass by the spring is calculated as;
F = kx(t)
F = kx(3.3)
F = 5,210.8 N/m x 1.2 m
F = 6,252.96 N
The complete question is below:
A 0.33 kg mass on a spring has a frequency of 20 hz and an amplitude of 1.2 m, then find the force the spring puts on the mass 3.3 seconds after.