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Having trouble with the following problem:

A small particle slides along the bottom of a 10 inch radius circular bowl. Neglect friction and assume small oscillations. If the particle has a speed of 15 in/s when it is at the bottom of the bowl, determine

a. The differential equation governing the motion

b. The period and amplitude of the resulting vibration

c. The position of the particle as a function of time

So far I've got:

a

Since a = dv/dt and v= r##\dot Θ##

d/dt (r##\dot Θ##) = gcosΘ

r##\ddot Θ## -gcosΘ = 0

##\ddot Θ## -g/r cosΘ= 0

To me this looks like a second order differential equation. I'm taking differential equations now and not doing too well in the class, so I'm struggling. Plus, I don't think we've had one like this in class yet.

A small particle slides along the bottom of a 10 inch radius circular bowl. Neglect friction and assume small oscillations. If the particle has a speed of 15 in/s when it is at the bottom of the bowl, determine

a. The differential equation governing the motion

b. The period and amplitude of the resulting vibration

c. The position of the particle as a function of time

So far I've got:

a

_{t}= gcosΘSince a = dv/dt and v= r##\dot Θ##

d/dt (r##\dot Θ##) = gcosΘ

r##\ddot Θ## -gcosΘ = 0

##\ddot Θ## -g/r cosΘ= 0

To me this looks like a second order differential equation. I'm taking differential equations now and not doing too well in the class, so I'm struggling. Plus, I don't think we've had one like this in class yet.