- #1
UrbanXrisis
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a 1 kg mass attached to a spring with a force constant of 25 oscillates on a horizontal, frictionless track. At time t=0, the mass is released from rest at x=-3cm (the spring is compressed by 3cm). Find (a) the period of its motion. b) the max values of speed and acceleration. c) the displacement, velocity, acceleration as a function of time.
a)
T=2\pi \sqrt{\frac{m}{k}}
T=2\pi \sqrt{\frac{1kg}{25N/m}}
T=1.257s
b)
v_{max}=\omega A=\sqrt{\frac{k}{m}}*A =\sqrt{\frac{25}{1}}*0.03=0.15m/s
a_{max}=\omega ^2 A=\frac{kA}{m} ={\frac{25}{1}}*0.03=0.75m/s^2
c)
x=-0.03cos25t
v=0.15sin25t
a=0.75cos25t
is this all correct?
a)
T=2\pi \sqrt{\frac{m}{k}}
T=2\pi \sqrt{\frac{1kg}{25N/m}}
T=1.257s
b)
v_{max}=\omega A=\sqrt{\frac{k}{m}}*A =\sqrt{\frac{25}{1}}*0.03=0.15m/s
a_{max}=\omega ^2 A=\frac{kA}{m} ={\frac{25}{1}}*0.03=0.75m/s^2
c)
x=-0.03cos25t
v=0.15sin25t
a=0.75cos25t
is this all correct?
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