quick reply needed  Q54,52,51,50,48,45,42,34,35,31,30,29,27,26,FROM HCVERMA SIMPLE HARMONIC MOTION

 

put up the questions

atleast a few if not all

Q  34 the pendulumn of  certain clock has time period 2.04s how fast or slow does the clock run during 24 hrs???

 

 

the pendulumn of colock has time period 2.04sec

now, no. of collision in 1 daY =24*3600/2

                                            =43200

but ,in each oscillation it is slower by (2.04-2.00)=0.04sec

in 1 day it is slower by =43200*0.04

                                   =1728/60

                                   =28.8

 

so the clock runds 28.8 min slower in 1 day

                                                             

Q 27

A block 1 kg is executing SHM of amplitude 0.1m on a surface under the restoring force of a sspring of spring constant 100 N/m. A block of mass 3 kg is gently placed on it at the instant it passes though the mean position .assuming that the 2 blocks move together ,find the frequency & the amplitude og the motiuon??????????????

 

sol

A=0.1m

total mass =3+1=4kg

(when both the blocks are moving together)

K=100N/m

T=24/100=2/5 sec

 

therefore F=5/2 sec

let at the mean position the block of mass1 kg i has velocity v,

KE=1/2mv²=1/2 kx²

 where x=amplitude =0.1 m

since 1/2 *1*v²=(1*2)*100(0.1)²

             Kv=1m/sec........................(1)

after the 3 kg block is placed on the 1 kg block the mass of the system will be 3+1=4 kg (taking block&spring as a system) for this mass there will be no exteranl force

(when the oscillation s takes place).

there fore momentum is conserved

 

1*v=4*v¹    (velocity of 4 kg block is v)

v¹=1/4 m/s [as v =1 m/s from eq 1)

 

now the 2 blocks have velocity 1/4 m/s at the mean position

KE=1/2mv²

    =(1/2)*4(1/4)²

     =1/2 *1/4

KE mean =(1/2)mv² (1/2)4x(1/4)²

                   =1/2*1/4

when the blocks are going to the external position ,there will be only PE

therefore

PE=1/2 kx²=1/2*1/4

 

since

1/4=100x²

x=1/400        (where x is the new amplitude)

 x=0.05m=5cm   ..........................answer