AP EAPCET 25-Aug-2021 Shift 1 Paper

(A) Time-period in spring-block system is given by, $T=2\pi \sqrt{\frac{m}{k}}$ If mass is doubled, $T'=2\pi \sqrt{\frac{2m}{k}}$ ⇒ $T'=\sqrt{2} T$ Hence, time period becomes $\sqrt{2}$ times, if the mass of the block is doubled. $(A \rightarrow 4)$ (B) For spring, $PE=\frac{1}{2} k x^{2}$ If spring constant is increased 4 times, PE becomes 4 times. $(B \rightarrow 3)$ (C) Speed of the block, $v=\omega A$ Hence, velocity of the block becomes twice when amplitude of the oscillation is doubled. $(C \rightarrow 2)$ (D) Energy of the oscillation, $E=\frac{1}{2} m \omega^{2} a^{2}$ $E'=\frac{1}{2} m \omega'^{2} a^{2}$ $\Rightarrow E'=\frac{1}{2} m (2\omega)^{2} a^{2}=\frac{4}{2} m \omega^{2} a^{2}$ $(\because)'=2\omega)$ ⇒ E' = 4E Energy of the oscillation becomes 4 times when angular frequency is doubled. $(D \rightarrow 1)$