Question

In: Physics

A mass of 0.30 kg is attached to a spring and set into oscillation on a...

A mass of 0.30 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.48 m)cos[(8 rad/s)t]. Determine the following.

(a) amplitude of oscillation for the oscillating mass. Answer in m

(b) force constant for the spring. Answer in N/m

(c) position of the mass after it has been oscillating for one half a period. Answer in m

(d) position of the mass one-third of a period after it has been released. Answer in m

(e) time it takes the mass to get to the position x = ?0.10 m after it has been released. Answer in s

Expert Solution

Mass

Displacement of mass as a function of time

(a)

Comparing the above equation with the equation for displacement of a particle in simple harmonic motion,

Amplitude of oscillation of mass .

(b)

Using the formula ,

Force constant of spring

(c)

Time period of oscillation

One half of a period is

Position at that time is

(d)

Time period of oscillation

One third of a period is

Position at that time is

(e)

position .

genius_generous answered 2 years ago

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