At an instant, an SHM oscillator has displacement y = A cos30°. The amplitude is 40 cm and kinetic energy is 200 J. If the spring constant is 1.0 × 10ˣ N m⁻¹, find x.

Question

G1 Physics · Accepted Answer

At the given instant: y = A cos30° = (√3/2)A For SHM: K = (1/2)k(A² - y²) = (1/2)k[A² - ( 3 4 \frac{3}{4} 4 3 ​ )A²] = (1/8)kA² Given K = 200 J and A = 0.40 m: 200 = (1/8)k(0.40)² k = 200×8/0.16 = 10⁴ N m⁻¹ Thus x = 4. Final value: 4