In the given diagram the threads, spring and pulleys are massless, no friction anywhere. Find the angular frequency of the system (in rad/sec). [Given K = 20 N m⁻¹ and m = 4 kg.]
Physics · Mixed Chapter
JEE Mains

Question

In the given diagram the threads, spring and pulleys are massless, no friction anywhere. Find the angular frequency of the system (in rad/sec). [Given K = 20 N m⁻¹ and m = 4 kg.]

G1 Physics · Accepted Answer

Step 1: The inclined mass is connected through the rope and one movable pulley to a second equal mass. If the incline mass moves distance x along the spring, the hanging mass moves x/2. Step 2: Ignoring static offsets, kinetic energy is ½mẋ² +½m(ẋ/2)²=½(5m/4)ẋ². The only elastic energy is ½Kx². Step 3: Thus ω²=K/(5m/4)=4K/(5m). Step 4: With K=20 N m⁻¹ and m=4 kg, ω²=4 and ω=2 rad s⁻¹.