. There is a small gap XY at the ends of the wire at the top of the frame. The frame is suspended so that it hangs vertically using thin cotton thread attached to the two ends of the wire. The frame oscillates about its vertical axis, as shown in the view from above in Figure 6.2.

Figure 6.2, a view from above showing the rectangular frame's equilibrium position (dashed line) and two extreme positions of its oscillation (solid and dotted lines) about the vertical axis, with the angle $s$ marked between the equilibrium line and one extreme

The oscillations are simple harmonic. The displacement

s

of the edge of the frame from its equilibrium position varies with time

t

according to

s = 3.2 sin (6.9 t)

where

s

is in mm and

t

is in s. Calculate the period

T

of the oscillations.

6(b)(ii)Simple Harmonic MotionEasy2 marks

Show that the maximum speed of the edges of the frame is

22 mm s^{- 1}

Draw with the mouse or a finger.

6(c)(i)Electromagnetic Induction GeneratorsMedium3 marks

The frame in 6(b) is in a uniform horizontal magnetic field that is parallel to the equilibrium position of the frame. The flux density of the magnetic field is

0.047 T

. Calculate the electromotive force (e.m.f.)

E_{0}

induced across XY when the frame is moving at its maximum speed.

6(c)(ii)Electromagnetic Induction GeneratorsEasy2 marks

On Figure 6.3, sketch the variation of the induced e.m.f.

E

across XY with

t

between

t = 0

and

t = 2 T

Draw with the mouse or a finger.