The question is simple, yet neither me nor my classmate can get it: A mass-sprin

Question

The question is simple, yet neither me nor my classmate can get it:

A mass-spring system with a natural frequency of 4.4 Hz is started in motion with an initial displacement from equilibrium of 5.7 cm and an initial velocity of 1.4 m/s. What is the amplitude of the resulting motion?

So I assume this question is telling me that a system that oscillates at 4.4 Hz is dispalced said amount but also pushed when released at 1.4 m/s. I think the solution requires the use of energy of the system, but my attemps have failed. Can anyone solve this and explain this to my troubled mind?

Explanation / Answer

let

X= A cos( wt+ @)

where w= angular freq

A= amplitude

@ = phase

given x(0) = A cos @ = 5.7 cm = 0.057 meter......(1)

V = dx/dt = -Aw sin (wt+@)

V(0) = -Aw sin @ = 1.4

but w= 2*3.14*4.4 = 27.632

V(0)/x(0) = -w tan @ = 24.561

tan @ = -0.889

@ = -41.663

substitute in (1)

we get

A= 0.057/cos@ = 7.63 cm

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