Question

Suppose a spring with spring constant 9 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 0.9 Hz (cycles per second). What is the mass? Assume there is no friction.

Answer 1

Answer:

m = 0.3 kg

Explanation:

• Assuming no friction present, the only force acting on the mass (in the horizontal direction) is the spring force.
• This force obeys the Hooke's Law, so we can write:

        $F = -k*x$

• At the same time, this net force must meet the Newton's 2nd law, at any moment:

       $F = m*a$

• When we have a movement when acceleration is inversely proportional to the displacement, we have a SHM, with an angular frequency defined as follows:

        $\omega = \sqrt{\frac{k}{m} } = 2*\pi *f = \sqrt{\frac{k}{m}}$

• Taking squares at both sides, we arrive to the following equation:

        $4*\pi ^{2} *f^{2} = \frac{k}{m}$

• So, replacing by our givens (k and f), we can solve for m, as follows:

        $m = \frac{k}{4*\pi ^{2}*f^{2} } =\frac{9N/m}{4*\pi^{2}*(0.9(1/s))^{2} } = 0.3 kg$

• The mass is 0.3 kg.