Q13.10: NCERT Physics - Part 2 OSCILLATIONS 13.10 Solution: In Exercise 13.9, let us take the position of mass when the…

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Q13.10: NCERT Physics - Part 2 OSCILLATIONS 13.10 Solution: In Exercise 13.9, let us take the position of mass when the…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often treat the minus sign in $-A\cos(\omega t)$ as a change in amplitude rather than a $\pi$ phase shift, and they may choose $\sin$ or $\cos$ arbitrarily without matching the given initial displacement and velocity. Always determine the phase by applying the initial conditions: $x(0)$ fixes the phase (e.g., $x(0)=0$ ⇒ sine form, $x(0)=\pm A$ ⇒ cosine with appropriate sign), while the amplitude $A$ and angular frequency $\omega$ remain unchanged.

In Exercise 13.9, let us take the position of mass when the spring is unstretched as x = 0, and the direction from left to right as the positive direction of x-axis. Give x as a function of time t for the oscillating mass if at the moment we start the stopwatch (t = 0), the mass is (a) at the mean position, (b) at the maximum stretched position, and (c) at the maximum compressed position. In what way do these functions for SHM differ from each other, in frequency, in amplitude or the initial phase?