Answer:
a) x=0 %T=0, b) x= A %T=100%, c) x=-A %T=50%
Explanation:
This is a simple harmonic movement exercise, which is explained by the expression
x = A cos (wt + Ф)
where angular velocity is related to frequency and period
w = 2π f = 2π / T
we can write the equation of the oscillation
x = A cos θ
When seeing the two equations they are equivalent, so what happens with the angle will also happen with time
We are asked for the percentage of the period at three points: at the maximum elongation and at the point of x = 0, in general the distance is measured from the point of the spring without stretching
The period is defined as the time that the system takes to give a complete oscillation, that is, from x = 0 to x = A and return
a) for the unstretched spring point x = 0
In general, both distance and time are measured from this point, so the percentage of time is zero.
% T = 0
b) for x = A
let's find the angle
cos tea = x / A = 1
therefore the angles tea = 2π rad
when the movement reaches the point of 2π radians it begins to repeat so the period is complete
% T = 100%
c) the point of maximum compression x = -A
let's look for the angles
cos tea = x / A = -1
therefore the angles tea = π rad
at this point the movement is halfway so it should take half the time
% T = 50%
