A block of mass m oscillates on a horizontal spring with time period t. Now a uniform electric field is switched on find the new time period
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I'm having a lot of trouble trying to figure this out: a box of mass m and positive charge Q is attached to a spring of spring constant k, which is in the equilibrium position. They sit horizontally on a table, with the box to the right of the spring. The other end of the spring is attached to a wall. The whole setup is immersed in a uniform electric field E, which points rightward, away from the spring, so that when the box moves the spring is stretched.
I'm not sure exactly what happens in this situation. I thought the box stopped moving when the spring force and electric force were equal, but then I realized that of course the box still has inertia and will move along at a constant speed. But then the spring will continue to cause it to accelerate... right? Does that mean it oscillates back and forth at a new point of equilibrium?
Also, how can you find the maximum amount the spring is stretched? It seems like you'd have to use calculus, but this problem is from an algebra-based textbook. (I only know a tiny amount of calculus).
The only way I can think of to solve this problem is setting the spring potential energy at x equal to the electric potential energy... but since the field is uniform, the electric potential energy is infinite, right?
(If it's any use to anyone, this is problem 9, Chapter 16, page 593 in Serway Vuille College Physics, Tenth Edition.)