A mass suspended from a spring oscillates in simple harmonic motion.

Question

A mass suspended from a spring oscillates in simple harmonic motion. The mass completes 2 cycles every second, and the distance between the highest point and the lowest point of the oscillation is 14 cm. Find an equation of the form y = a sin 𝜔t

 that gives the distance of the mass from its rest position as a function of time.

Answer 1

If the mass completes 2 cycles every second, then (I assume full cycles) it has the frequency 2 s -¹ (Hz). Frequency is equal to the number of cycles in a unit of time.

Knowing that the distance between the lowest and highest points is 14 cm, we can find that amplitude of oscillations is 7 cm.

In general form the equation of oscillations looks like this

y = A·sin ( ωt + ϕ₀).

Where

y – is displacement at any given time,

A – amplitude of oscillations,

ω= 2πf – cyclic frequency,

ϕ₀ – initial phase.

Now we can get an answer, assuming that initial phase is 0

                            y = 7sin (2π∙2t + 0)

Or finally                                               y = 7∙sin(4π t), cm