i am very stuck on this problem, i am not given much info so i dont know what equations to use
A particle undergoes simple harmonic motion with amplitude 29 cm and maximum speed 4.8 m/s
how do i find the angular frequency. and the maximum acceleration
A particle undergoes simple harmonic motion with amplitude 29 cm and maximum speed 4.8 m/s
how do i find the angular frequency. and the maximum acceleration
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I'm not sure fi you have been given these equations in class yet but I would use this:
v(t)=-ω(xmax)sin(ωt+Φ)
-ω is the angular frequency
-xmax is the amplitude (maximum x value) which is given
This equation tells you the velocity at any point in time. You already know the MAX velocity is 4.8 m/s.
You should also realize that the velocity amplitude(vmax) is:
vmax=ω(xmax)
You know both vmax and xmax, so solve for ω (angular frequency)
To solve for amax, you use the equation for acceleration as a function of time, which is:
a(t)=ω^2(xmax)cos(ωt+Φ)
In this case, similar to the case above, amax=ω^2(xmax)
You know both ω and xmax now, so solve for amax.(remember to convert your xmax to meters)
This stuff can get confusing, especially since im typing it over the internet rather than explaining it. I hope this helps though. Please let me know.
v(t)=-ω(xmax)sin(ωt+Φ)
-ω is the angular frequency
-xmax is the amplitude (maximum x value) which is given
This equation tells you the velocity at any point in time. You already know the MAX velocity is 4.8 m/s.
You should also realize that the velocity amplitude(vmax) is:
vmax=ω(xmax)
You know both vmax and xmax, so solve for ω (angular frequency)
To solve for amax, you use the equation for acceleration as a function of time, which is:
a(t)=ω^2(xmax)cos(ωt+Φ)
In this case, similar to the case above, amax=ω^2(xmax)
You know both ω and xmax now, so solve for amax.(remember to convert your xmax to meters)
This stuff can get confusing, especially since im typing it over the internet rather than explaining it. I hope this helps though. Please let me know.