x-t equation of a particle in SHM is given as x = 1.0 sin ( 12 π t ) : in SI units. Potential energy at mean position is zero. Mass of the particle is 4 1 Kg . List - I List - II (P) Frequency with

Question

x-t equation of a particle in SHM is given as $x = 1.0 sin (12 π t)$ : in SI units. Potential energy at mean position is zero. Mass of the particle is $\frac{1}{4} Kg$ .

List - I	List - II
(P) Frequency with which kinetic energy oscillates	(1) $\frac{1}{2}$
(Q) Speed of particle is maximum at time $t =$	(2) $18 π^{2}$
(R) Maximum potential energy	(3) 12
(S) Force constant K	(4) $36 π^{2}$
	(5) None of these

TestHub · Accepted Answer

Here ω = 12 π , A = 1 , m = 4 1 ​ kg. (P) KE oscillates at twice the oscillation frequency: 2 f = 2 π 2 ω ​ = 12 - 3. (Q) Speed is maximum when x = 0 , i.e. 12 π t = nπ ⇒ t = 12 n ​ ; both t = 2 1 ​ (n=6) and t = 12 qualify - 1, 3. (R) P E ma x ​ = 2 1 ​ m ω 2 A 2 = 2 1 ​ ⋅ 4 1 ​ ⋅ 144 π 2 = 18 π 2 - 2. (S) K = m ω 2 = 36 π 2 - 4. Hence option (B).

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