Question

if a body of mass 36 grams moves with S.H.M of amplitude A=13cm and period T=12sec.At a time t=0 the displacement is x=+13cm.The shortest time of passage from x=+6.5cm to x=-6.5 is
​

Answer 1

Answer:

The equation of the SHM is:-

y=Acosωt where A=13cm and

T

2π

as T=125,⇒ω=

12

2π

=

6

π

rad/s

also at t=0,y=13 as given

=y=13cos(

6

πt

) ⇒t=

π

6

cos

−1

(

13

y

)

when particle is at y=6.5 ,time is,

t

1

=

π

6

cos

−1

(

13

6.5

)=

π

6

×

3

π

=25

also when y=−6.5, time is :-

t

2

=

π

6

cos

−1

(

13

−6.5

)=

π

6

×

3

2π

=45

∴ Time difference Δt=t

2

−t

1

=(4−2)=2s

Explanation:

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Answer 2

Answer:

02sec

Explanation:

The equation of the SHM is:-

y=Acosωt where A=13cm and T2π​

as  T=125,⇒ω=122π​=6π​rad/s

also at t=0,y=13 as given

=y=13cos(6πt​)  ⇒t=π6​cos−1(13y​)

when particle is at y=6.5 ,time is,

t1​=π6​cos−1(136.5​)=π6​×3π​=25

also when y=−6.5, time is :-

t2​=π6​cos−1(13−6.5​)=π6​×32π​=45

∴ Time difference Δt=t2​−t1​=(4−2)=2s