Rope with a length b and a constont speed in the spape the perdulum connected to q mass m is shor tened at f de=-cl> o)tlonging point is fixed, write the lagronge equation in terms of m, b,,e final equators of motion 9t ony instont e ti)shaw that at the time te 3bo the vilbrartion frequency w 4x cloubles the initial value.

3. a worker pushes a 30.5 kg polished stone along a polished table with a force on bonin a straight line for 5.20 s after starting from rest. there is no friction between thestone and the table. at the end of the table. the stone is hooked to a cable with a lengthof 62.0 cm to rotate it to a rough table to store until they can be picked up. the roughtable has a coefficient of static friction 0.702 with the polished stone. remember that 8= 9.80 m/s2a) what is the speed of the stone when it is hooked to the cable? b) what is the tension in the cable while the stone is rotating? (there is still nofriction)c) how much force is needed to make the stone begin sliding from rest on therough table? ius = 0.70262.0 cm30.5 kg20.5 kg6= 0