For the mass–spring–pulley system shown, with mass m = 4 kg and spring constant K = 20 N m⁻¹, find the angular frequency in rad s⁻¹. Strings, spring and pulleys are ideal. [See Image.]
Physics · Mixed Chapter
JEE Main Practice

Question

For the mass–spring–pulley system shown, with mass m = 4 kg and spring constant K = 20 N m⁻¹, find the angular frequency in rad s⁻¹. Strings, spring and pulleys are ideal. [See Image.]

G1 Physics · Accepted Answer

Step 1 — Choose the motion of the block as generalized displacement x; use the inextensible-string constraints to express extension of spring Δs in terms of x. Step 2 — The effective spring potential is U = (1/2)K(Δs)² = (1/2)kₑff x², and effective kinetic energy is (1/2)mₑffẋ². Step 3 — Apply ω = √(kₑff/mₑff), with m = 4 kg and K = 20 N m⁻¹. Step 4 — Original arrangement gives the printed ω = 2 rad s⁻¹. [Exact pulley/string routing remains in Image.]