Question

14. Figure shows the velocity-time graph of an object executing SHM. The correct equation for displacement - time (x - t) representing this motion is [NCERT Pg. 345](1) X = 50 cos - t +cm(2) X = -50 sint cmTT(3) X=107 sint cm5TU(4) X = -10Tt sint cm5​

Answer 1

Explanation:

here's the attachment for solution

Answer 2

Answer:

Correct answer for the question is (1)- $50\cos(\frac{\pi}{5}t+\pi)$

Step by step solution:

Step 1: Required Knowledge

• The maximum displacement of SHM from mean position is called as amplitude (A).
• Equation of SHM is $x=A\sin\omega t$, where $\omega = \frac{2\pi}{T}$, T is time period
• Integration of velocity with time gives us displacement

Step 2: Calculating equation for displacement

From graph, it is clear that, A = 10π,

⇒ $v=10\pi\sin\frac{2\pi}{T} t$

⇒ $v=10\pi\sin\frac{\pi}{5} t$

⇒ $\int\limits \, dv = 10\pi\int\sin\frac{\pi}{5} t$

⇒ $x = \frac{-10\pi}{\frac{\pi}{5} }\cos\frac{\pi}{5} t$

⇒ $x = -50\cos\frac{\pi}{5} t$

⇒ $x = 50\cos(\frac{\pi}{5} t+\pi)$