1.00-kg glider attached to a spring with a force constant 16.0 N/m oscillates on

Question

1.00-kg glider attached to a spring with a force constant 16.0 N/m oscillates on a frictionless, horizontal air track. At t the glider is released from rest at x = -2.50 cm (that is; the spring is compressed by 2.50 cm). Find the period of the glider's motion. Find the maximum values of its speed and acceleration. Find the position, velocity, and acceleration as functions of time. (Where position is in m, velocity is in m/s, acceleration is in m/s2, and t is in s. Use the following as necessary: t.)

Explanation / Answer

a.)Time period= 2piesqrt(m/k)=2*3.14*sqrt(1/16)=1.57seconds.

b.)Vmax=Amplitude *omega=2.5/100*(2pie/T)= 0.1m/sec (w=sqrt(k/m)=2pie/T=4)

amax=Amplitude*omega*omega=2.5/100*4*4=0.4m/sec^2.

c.) x=Asin(wt+theta)=2.5/100sin(4t-90degrees) As it starts from negative coordinate,the phase would be -90 degrees.

v=dx/dt=Awcos(wt+theta)=2.5/100*4cos(4t-90)

a=dv/dt=-Aw^2sin(wt+theta)=-2.5/100*4*4*sin(2t-90degrees)

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