A mass of 1.1kg is attached to a spring and constrained to move without friction along...

A mass of 1.1kg is attached to a spring and constrained to move without friction along the x-axis. The mass is attached to a spring of spring constant 80?? N m ; one end of the spring is attached to a fixed point along the x-axis while the other is attached to the mass. The equilibrium position of the mass is the origin. The mass has a position as a function of time which can be expressed: ?(?)=?cos(??+?) x ( t ) = A cos ⁡ ( ω t + ϕ ) At ?=0? t = 0 s the mass is at position ?(0?)= x ( 0 s ) = 0.15m. The mass has a velocity at that time of ?(0?)=− v ( 0 s ) = − 1.13?? m s . What is the period of the resulting oscillation? Answer in seconds. What is the amplitude of the resulting oscillation? In other words what is ? A in the formula above. Answer in meters. What is the x-position of the mass at time ?=0.5? t = 0.5 s ? Answer in meters. Answer to the nearest mm; in other words your answer should have three decimal places. What is the total mechanical energy of the mass-spring system (kinetic and potential) at ?=0.75? t = 0.75 s ? Answer in Joules.

Solutions

Expert Solution

1) Period =5.4974 sec

2) Amplitude A= 0.2545m

3)Position at t= 0.5, x = 0.1479m or upto three decimal places 0.148 m.

4) Total Mechanical energy = 5.9906 J

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genius_generous answered 1 year ago

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