Please show all the steps 6. My Notes Ask Your Teach A mass of 0.560 kg is attac

Question

Please show all the steps

6. My Notes Ask Your Teach A mass of 0.560 kg is attached to a spring and set into oscillation o following. a horizontal frictionless surface. The simple harmonic motion of the mass is described by xtt) (0.700 m)cosl(14.0 rad/s)t). Determine the (a) amplitude of oscilation for the oscillating mass (b) force constant for the spring N/m (c) position of the mass after it has been oscillating for one half a period (d) position of the mass two-thirds of a period after it has been released (e) time it takes the mass to get to the position x 0.500 m after it has been released Additional Materials eBook Tutorial

Explanation / Answer

In general, x(t) = A cos(wt - o),

x = displacement (m)

A = amplitude (m)

w = angular frequency (radians/s)

t = time (s)

o = phase shift (radians)

Comparing with the equation provided,

(a) Amplitude of oscillation = 0.700 m

(b) Force constant 'k' can be determined using, w = sqrt( k / m )

k = w2m = (14 rad/s)2 x (0.560 kg) = 109.76 N/m

(c) Time period 'T' = (2 x pi) / w = 0.449 s

half of T = 0.2245 s

x(0.2245 s) = (0.700 m)cos[(14 rad/s)(0.2245 s)] = -0.699 m

(d) Two third of T = 0.299 s

x(0.2993 s) = (0.700 m)cos[(14 rad/s)(0.299 s)] = -0.352 m

(e) -0.500 m = (0.700 m)cos[(14 rad/s)(t)]

t = 0.169 s

Feel free to ask anything else and please support.

Thank You

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