An object is attached to a coiled spring. The object is pulled down (negative direction from the rest position) 88 centimeters, and then released. Write an equation for the distance d of the object from its rest position, after t seconds if the amplitude is 88 centimeters and the period is 44 seconds.
The equation for the distance d of the object from its rest position is
To find the equation for the distance d of the object from its rest position after t seconds, we can use the formula for simple harmonic motion:
d = A * cos(2π * t / T)
where:
d = distance from rest position
A = amplitude (maximum displacement from rest position)
t = time in seconds
T = period (time for one complete oscillation)
In this case, the amplitude A is given as 88 centimeters and the period T is given as 44 seconds.
Substituting the values into the formula, we get:
d = 88 * cos(2π * t / 44)
given by:
d(t) = A * cos(2π / T * t)
where:
d(t) = the distance of the object from its rest position at time t
A = the amplitude of the oscillation (in this case, 88 centimeters)
T = the period of the oscillation (in this case, 44 seconds)
t = time in seconds
Plugging in the values, we get:
d(t) = 88 * cos(2π / 44 * t)
period = 2π/k
k = 2π/44 = π/22
d = -88 sin ( (π/22)(t+11) )
must be a magic coiled spring, it never seems to lose its bounce.