For the simple harmonic motion equation [tex]$d=9 \cos \left(\frac{\pi}{2} t\right)$[/tex], what is the maximum displacement from the equilibrium position?

Answer here:
[tex]$\qquad$[/tex]



Answer :

To find the maximum displacement from the equilibrium position for the given simple harmonic motion equation [tex]\( d = 9 \cos \left( \frac{\pi}{2} t \right) \)[/tex], follow these steps:

1. Identify the Amplitude: The equation of simple harmonic motion provided is in the form [tex]\( d = A \cos(\omega t) \)[/tex], where [tex]\( A \)[/tex] is the amplitude and [tex]\( \omega \)[/tex] is the angular frequency. In our case, the equation is [tex]\( d = 9 \cos \left( \frac{\pi}{2} t \right) \)[/tex].

2. Maximum Value of Cosine Function: The cosine function [tex]\( \cos(x) \)[/tex] can take values between -1 and 1. Therefore, its maximum value is 1.

3. Calculate Maximum Displacement: The maximum displacement from the equilibrium position occurs when the cosine function attains its maximum value, which is 1.
[tex]\[ d_{\text{max}} = 9 \cdot 1 = 9 \][/tex]

Thus, the maximum displacement from the equilibrium position is:
[tex]\[ \boxed{9} \][/tex]