Question

One end of a light spring with force constant 290 N/m is attached to a vertical wall. A light string is tied to the other end of the horizontal spring. As shown in the following figure, the string changes from horizontal to vertical as it passes over a solid pulley of mass Mi the shape of a solid disk of radius R = 1.50 cm. The pulley is free to turn on a fixed smooth axle. The vertical section of the string supports an object of mass m = 370 g. The string does not slip at its contact with the pulley. The object is pulled downward a small dista and released. (a) What is the angular frequency w of oscillation of the object in terms of the mass M? w = rad/s (b) What is the highest possible value of the angular frequency of oscillation of the object? rad/s (c) What is the highest possible value of the angular frequency of oscillation of the object if the pulley radius is doubled to R = 3 cm? rad/s

Answer 1

@ Apply Hooke's law, F+Kx = 0 - 0 mg-T' = m d²x dz2 R17'-1) = 3 MR to T-T = 2 m d 2x (m+3M) dan mg -T T= -(m+ 12 M) dan ting d 2-2 o o W o r = 2 mm es fago - 14.45) vadis w= 14.45 radls (of Pulley radius is increased the frequency will not effect & co reman same).