Question

what are the extreme position and condition v a and z​

Answer 1

Answer:

When a particle starts from an extreme position , it is useful to write the motion law as

x=acosωt (1)

(However x is the displacement from the equilibrium position)

It t

1

be the time to cover the distance e/2 then from (1)

a−

2

a

=

2

a

=acosωt

1

or cosωt

1

=

2

a

=cos

3

π

(as t

1

<T/4)

Thus

t

1

=

3ω

π

=

3(2π/T)

π

=

6

T

As

x=acosωt, so v

x

=−aωsinωt

Thus

v=∣v

x

∣=−v

x

=aωsinωt, for t≤t

1

=T/6

Hence sought mean velocity

<V>=

∫dt

∫vdt

=∫

0

T/6

a(2π/T)sinωtdt/T/6=

T

3a

=0.5 m/s