Answer:
The maximum displacement from the equilibrium position is 9.
Step-by-step explanation:
The given simple harmonic motion is:
[tex]d=9cos(\frac{\pi}{2}t)[/tex]
Differentiating above equation with respect to t, we get
[tex]d'=-9sin(\frac{\pi}{2}t)(\frac{\pi}{2})[/tex]
⇒[tex]d'=-\frac{9{\pi}}{2}sin(\frac{\pi}{2}t)[/tex]
Again differentiating the above equation with respect to t, we have
[tex]d''=-\frac{9({\pi})^{2}}{4}cos(\frac{\pi}{2}t)<0[/tex]
Now, [tex]d'=0[/tex]
⇒[tex]-\frac{9{\pi}}{2}sin(\frac{\pi}{2}t)=0[/tex]
⇒[tex]sin(\frac{\pi}{2}t)=0[/tex]
⇒[tex]\frac{\pi}{2}t=0[/tex]
⇒[tex]t=0[/tex]
Substituting the value of t=0 in d, we get
⇒[tex]d=9cos(\frac{\pi}{2}(0))[/tex]
⇒[tex]d=9cos(0)[/tex]
⇒[tex]d=9(1)[/tex]
⇒[tex]d=9[/tex]
Therefore, the maximum displacement from the equilibrium position is d= 9.
