q.1A horozontal platform vibrates up & down with a SHM of frequency 2 / pai HZ. find the max permissible amplitude so that an object kept on the platform remain in contact with platform.

x = A sinwt

a (accleration) = -Aw²sinwt

maximum accleration = -w²A

when this accleration is just equal to accleration due to gravity then particle is about to leave

the surface ...if accleration is more than this value then it will loose the contact

w²A = g

A = g/W²               ....................1

w = 2pif

f = 2/pi so

w = 4radiansec^-1

A = g/4² = 10/16 = 0.625m                            (g = 10m/s²)

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Approved