Answer:
d=\(5\)
Step-by-step explanation:
The given simple harmonic motion equation is given as:
d=\(5sin(2{\pi}t)\)
Differentiating the above equation with respect to t, we have
\(d'=5cos(2{\pi}t)(2{\pi)\)
\(d'=10{\pi}cos(2{\pi}t)\)
Now, equating \(d'=0\), we have
\(10{\pi}cos2{\pi}t=0\)
\(cos2{\pi}t=0\)
\(2{\pi}t=\frac{{\pi}}{2}\)
\(t=\frac{1}{4}\)
Also, differentiating again with respect to t, we get
\(d''=10{\pi}(-sin(2{\pi}t)(2{\pi})\)
⇒\(d''<0\)
Therefore, at t=\(\frac{1}{4}\), d=\(5sin(2{\pi}t)\) will have maximum displacement.
⇒d=\(5sin(2{\pi}(\frac{1}{4}))\)
⇒d=\(5sin(\frac{\pi}{2})\)
⇒d=\(5\)
