Write an equation with phase shift 0 to represent simple harmonic motion with initial position -1/2, amplitude 1/2, and period 4.
I got d=(1/2) sin (pi/2) t + (1/2).
Is this correct?
The initial position (at t=0) is not -1/2
Or is that initial - just a separator?
Also, if you're going to use parentheses, it ought to be
d = 1/2 sin(pi/2 t) - 1/2
To express a simple harmonic motion equation with a phase shift of 0, initial position of -1/2, amplitude of 1/2, and period of 4, you need to use the general form of a simple harmonic motion equation:
d = A sin(wt - φ) + d₀
Where:
d is the position at any time t
A is the amplitude
w is the angular frequency (w = 2π / T, where T is the period)
φ is the phase angle (in this case, 0 since there is no phase shift)
d₀ is the initial position
Given that the amplitude (A) is 1/2 and the period (T) is 4, we can calculate the angular frequency (w):
w = 2π / T = 2π / 4 = π/2
Plugging in the values into the equation, we get:
d = (1/2) sin((π/2) t - 0) - 1/2
Simplifying the equation, we have:
d = (1/2) sin((π/2) t) - 1/2
Therefore, the correct equation for the given conditions is:
d = (1/2) sin((π/2) t) - 1/2
So, your answer of d = (1/2) sin((π/2) t) + 1/2 is incorrect, as there is no phase shift in the given problem.