A mass m is attached to a spring of force constant 78.0 N / m and allowed to osc

Question

A mass m is attached to a spring of force constant 78.0N/m  and allowed to oscillate. The figure (Figure 1) shows a graph of its velocity vx as a function of time t

A) Find the period.

B)Find the frequency and the angular frequency of this motion.

A mass m is attached to a spring of force constant 78.0N/m and allowed to oscillate. The figure (Figure 1) shows a graph of its velocity vx as a function of time t Find the period. Find the frequency and the angular frequency of this motion. Please enter your answers in the order frequency, angular frequency separated with comma. What is the amplitude (in cm)? At what times does the mass reach the position x= plusminus A? If there is more than one value, please enter your answers in ascending order separated with commas. Find the maxi mu m acceleration of the mass. Find the times at which the maxi mu m acceleration occurs. If there is more than one value, please enter your answers in ascending order separated with commas. What is the mass m ?

Explanation / Answer

a) Period, T = 1.6 s

b) frequency, f = 1/T = 1/1.6 = 0.625 Hz

    Angular frequency, w = 2*pi*f = 3.935 rad/s

    0.625, 3.935

c) maximum velocity = A*w

A = v/w = 0.20/(3.927) = 0.0509 m

d) At following time, it reaches maximum positions: 0.4 s , 1.2 s, 2.0 s, ....

e) a = A * w^2 = 0.0509* 3.927 * 3.927 = 0.785 m/s^2

f) At following time, it reaches maximum acceleration: 0.4 s , 1.2 s, 2.0 s, ....

g) w = sqrt (k/m)

   mass = k/w^2 = 78/( 3.927 * 3.927 ) = 5.06 Kg

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