An object attached to a spring vibrates with simple harmonic motion as described

Question

An object attached to a spring vibrates with simple harmonic motion as described by the figure below.

For this motion, find the following.
(a) the amplitude
. cm

(b) the period
.
Your response differs from the correct answer by more than 10%. Double check your calculations. s

(c) the angular frequency
rad/s

(d) the maximum speed
.
Your response differs from the correct answer by more than 10%. Double check your calculations. cm/s

(e) the maximum acceleration
cm/s2

(f) an equation for its position x in terms of a sine function (Do this on paper. Your instructor may ask you to turn in this work.)

Explanation / Answer

This is a graph oriented problem:
a) Amplitude means the maximum displacement traveled by the particle.
In the graph u look at the maximum point of the curve. This point corresponds to 2cm in the Y direction which is your displacement. SO AMPLITUDE = 2cm [ANS]

b) Period is the time taken to start from one place and return to that same place.
T= 4 seconds
c) angular frequency will be =2 p/T taking T = 4 s we get = p/2 rad/s

d) Maximum speed v = angular frequency X amplitude = 3.142 cm/s

e) Maximum acceleration = [angular frequency]^2 X amplitude = 4.935 cm/s^2

f) x = 2 sin(p/2t)

 

a)A=2cm (highest point on graph)
b) T=4s (time to complete a whole wave--up downup)
c) =2/T
       =2/4
       =/2 rad/s =1.57rad/s

d)vmax=A
            =2*/2
            = cm/s =3.142 cm/s

e) amax=A2
             =2*(/2)2
                  =2/2
              =4.92 cm/s2

f) eq: x(cm)=Asint
         =2sin(t/2)

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