A 0.39-kg mass is attached to the end of a spring and set into oscillation on a

Question

A 0.39-kg mass is attached to the end of a spring and set into oscillation on a horizontal frictionless surface by releasing it from a compressed position. The record of time is started when the oscillating mass passes through the equilibrium position and the position of the mass at any time is shown in the drawing.

Determine the following.

(a) amplitude A of the motion
______m

(b) angular frequency
_____rad/s

(c) spring constant k
_____N/m

(d) speed of the object at

t = 2.0 s

_______m/s

(e) magnitude of the object's acceleration at

t = 2.0 s

______m/s2     

Question 2

Find the ratio of the new/old periods of a pendulum if the pendulum were transported from Earth to Mercury, where the acceleration due to gravity is 3.70 m/s2.

= _____  

PLEASE ANSWER ALL THE QUESTIONS AND DONT GIVE WRONG ANSWERS THANKS FOR YOURR HELP !

Explanation / Answer

According to the given problem,

(a) From the graph, the amplitude is A = 0.10 m

(b) From the graph, the period T = 8 s, so
= 2/T = 2 / 8s = 0.79 rad/s

(c) From = (k/m) we get
k = m² = 0.39kg * (0.79rad/s)² = 0.2434 kg/s² = 0.2434 N/m

(d) From the graph, t = 2 s is a maximum of x, and so speed = 0 m/s.

(e) a = kx / m = 0.2434kg/s² * 0.10m / 0.39kg = 0.06241 m/s²

Only 4 subparts per question.

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