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