Tutorial 4SolutionsPhys 131October 15, 2021Problem 1a)EKis proportional tov2. The magnitude of the velocity is maximum att= 0, sincethe displacement is zero at that time. So, theEKmust be maximum att= 0, whichis only true in option ‘c’.b)EK,max=12mω2A2.Thus,T=2πω= 2πqmA22EK,max.Substituting in the values form, A, EK,maxwe get,T= 0.22s.Problem 2a) For a simple pendulum with lengthL, given acceleration due to gravity isg, the timeperiodT= 2πqLg. Thus for the same pendulum, the ratio of time periods at Earthand Mars isTETM=qgMgEand thusgM=gE(TETM)2.Plugging in the values, we getgM= 3.67ms-2.b) For small oscillations, time period of a pendulum is proportional to the square root ofits length, and is independent of its mass. Thus, to reduce the time period from 2.45s to 1 s, we need to reduce the length. The mass need not be changed as it does notaffect the time period, and the amplitude of oscillation must be kept small.Problem 3a) Damping decreases the oscillation frequency, thereby increasing the period. So, without