Question

A mass m= 1.0 kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion .The spring constant is 500 N/m. What is the amplitude A of the motion , so that the mass m tends to get detached from k the pan?(take g = 10m/s^2). The spring is stiff enough so that it does not get distorted during the motion.

Answer 1

@ganeshie8 @ParthKohli

Answer 2

i got N+kx0=mg -> 1
N+k(x+x0)-mg = ma
=>kx=ma -> 2 [substituting 1]
as this doesn't involve N.. how to proceed?

Answer 3

Condition for the mass to not detach from the pan :

\(a_{shm} \lt g\)

Answer 4

@ganeshie8 how did u get this condition?

Answer 5

@rvc

Answer 6

Condition for detach of the mass is that normal reaction of the block given by the pan should be equal to 0

Answer 7

ya i know that..did u see my first post? @samigupta8 but i don't seem to get an eq with N..(see abv.)

Answer 8

pri

here \(N = 0\) at the limit when the pan is just about to be moving faster than the weight

max accel occurs at the extreme end of the oscillation, as the motion changes direction. the pan accelerates faster than weight, ie faster than gravity....so the move apart and N = 0

so for simple case \(x = A \sin \omega t \) , you have \(\ddot x = - \omega^2 A \sin \omega t, | \ddot x_{max} |= \omega^2 A\) and so you want \( - \omega^2 A = - g\).

Answer 9

oh ok...now i understood..! thank you @IrishBoy123!