The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A / 2, the kinetic energy of the block is

Question

The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A / 2, the kinetic energy of the block is (A) 18.75 J (B) 37.5 J (C) 9.75 J (D) 12.5 J

Tardigrade Admin · Accepted Answer

u max =(1/2) m ω2 A 2=25 J KE at ( A /2)=(1/2) m v12=(1/2) m ω2(A2-(A2/4)) KE =(1/2) m ω2 (3 A 2/4)=(3/4)((1/2) m 2 A 2) KE =(3/4) × 25=18.75 J

Q. The maximum potential energy of a block executing simple harmonic motion is $25 J$ . A is amplitude of oscillation. At $A /2$ , the kinetic energy of the block is

$18.75 J$

$37.5 J$

$9.75 J$

$12.5 J$

$u_{m a x} = \frac{1}{2} m ω^{2} A^{2} = 25 J$
$K E$ at $\frac{A}{2} = \frac{1}{2} m v_{1}^{2} = \frac{1}{2} m ω^{2} (A^{2} - \frac{A ^{2}}{4})$
$K E = \frac{1}{2} m ω^{2} \frac{3 A ^{2}}{4} = \frac{3}{4} (\frac{1}{2} m^{2} A^{2})$
$K E = \frac{3}{4} \times 25 = 18.75 J$

Q. The maximum potential energy of a block executing simple harmonic motion is 25J. A is amplitude of oscillation. At A/2, the kinetic energy of the block is

18.75J

37.5J

9.75J

12.5J