Problem 6. A mass-spring system has position function x(t) e2 (2 cos(5t) + 3 sin(5t)) in...

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Problem 6. A mass-spring system has position function x(t) e2 (2 cos(5t) + 3 sin(5t)) in which positive values of x mean the spring is stretched and negative values mean the spring is compressed. Assume the mass only began moving at t = 0. a) Find the first moment when the mass passes through the equilibrium. b) Find when the mass will change the direction the first and the second time. c) Find when the spring will be stretched the most and when it will be compressed the most. Remark: the amplitude will be decreasing, so you only need to find the first time when the mass will be in the lowest position, and the first time when it will be in the highest position. Problem 6. A mass-spring system has position function x(t) e2 (2 cos(5t) + 3 sin(5t)) in which positive values of x mean the spring is stretched and negative values mean the spring is compressed. Assume the mass only began moving at t = 0. a) Find the first moment when the mass passes through the equilibrium. b) Find when the mass will change the direction the first and the second time. c) Find when the spring will be stretched the most and when it will be compressed the most. Remark: the amplitude will be decreasing, so you only need to find the first time when the mass will be in the lowest position, and the first time when it will be in the highest position.