Write the equation for simple harmonic motion (x-t),(v-t), and find v at t=2s and t=3s if the object is initially at the right extreme of origin and moving in the negative x-direction. (A=2cm, T=8s)

Explanation:

T = 8 s

angular frequency ω = 2π / T

= 2 π / 8

= π / 4

x ( t ) = A ( sinωt + π / 2 ) because initial phase difference is π / 2

= A cos ωt

= A cos π t / 4  

v = Aω sinωt

= 2 x π / 4 sinωt

= .5 π sinπt / 4

when t = 2

v = .5 π sinπ x 2 / 4

= .5 π x 1

= 1.57  cm /s

At t = 3 s

v = .5 π sin π x 3 / 4

= .5 π sin 135°

= .5 π / √ 2

= 1.11 cm /s

the answer is the first electromagnet (a). this is because it has more coils around the ferromagnetic material. increasing the number of coils increases the surface area in which the metal interacts with the current in the coil. this enables more atoms in the metal to become aligned hence becoming more magnetized.

the answer should be in the picture.