Question

(1 point) Suppose a spring with spring constant 1 N/m is horizontal and has one end attached to a wall and the other end attached to a mass. You want to use the spring to weigh items. You put the spring into motion and find the frequency to be 1.4 Hz (cycles per second). What is the mass? Assume there is no friction.

Answer 1

Step-by-step explanation:

Given that,

The spring constant

K = 1N/m

Frequency of motion

f = 14Hz

We want calculate the mass m?

The frequency of spring system is related to the mass by

From w = √k/m

Where w = 2πf

f = 1/2π √k/m

Where,

w is angular frequency in rad/s

m is mass of object attached in kg

k is the spring constant in N/m

f Is the frequency in Hz

Then, make m subject of formula

Multiply both sides by 2π

2πf = √k/m

Square both sides

4π²f² = k/m

Then, k= 4π²f² × m

m = k / 4π²f²

m = 1 / (4π² × 1.4)

m = 1 / 55.27

m = 0.0181 kg

m= 18.1 g

The mass of the object attached in 18.1 g or 0.0181 kg