A mass of 0.30 kg is attached to a spring and set into oscillation on a horizont

Question

A mass of 0.30 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by x(t) = (0.46 m)cos[(14 rad/s)t]. Determine the following.

(a) amplitude of oscillation for the oscillating mass = .46 m

(b) force constant for the spring = 58.8 N/m

(c) position of the mass after it has been osciallating for one half a period = -.459

----------- I need to figure out (d) and (e) Please help!

(d) position of the mass one-third of a period after it has been released

units in m

(e) time it takes the mass to get to the position x = ?0.10 m after it has been released

units in s

Explanation / Answer

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. Ifthis helps then kindly rate 5-stars.

A mass of 0.30 kg is attached to a spring and set into oscillation on a horizontal frictionless surface. The simple harmonic motion of the mass is described by

x(t) = (0.48 m)cos[(14 rad/s)t].

Determine the following.

(a) amplitude of oscillation for the oscillating mass
m

(b) force constant for the spring
N/m

(c) position of the mass after it has been oscillating for one half a period
m

(d) position of the mass one-third of a period after it has been released
m

(e) time it takes the mass to get to the position

x = ?0.10 m

after it has been released

Answer

x=A cos wt..............General equation

**********************************

a)

Amplitude= 0.48 m

*******************************

b)

w=14 rad/s

k=mw^2=0.3*14^2=58.8 N/m

*********************************

c)

T=2*pi/w

T(half)=pi/w

Substituting in x(t) = (0.48 m)cos[(14 rad/s)t].

x=0.48 * cos pi = -0.48 m

******************************************************

d)

T=2*pi/w

T(0n2-third)=2pi/(3w)

Substituting in x(t) = (0.48 m)cos[(14 rad/s)t].

x=0.48 * cos 2pi/3 = - 0.239 m

*******************************************************

e)

x=-0.1 m

Substituting in x(t) = (0.48 m)cos[(14 rad/s)t].

14t = cos-1(-0.1/4.8)=1.59

t=0.11 seconds

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