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 10 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

The equation of the distance of the mass from its rest position as a function of time is y = 10 sin(2πt).

Step-by-step explanation:

To find the equation of the distance of the mass from its rest position as a function of time, we can use the formula for simple harmonic motion: y = a sin(ωt). In this case, the mass completes 2 cycles every second, which means the frequency (ω) is 2π radians per second. The distance between the highest and lowest points of the oscillation is the amplitude (a), which is given as 10 cm. Therefore, the equation for the distance of the mass from its rest position as a function of time is y = 10 sin(2πt).