How does the first equation (for t=0 and x=0) have a cos and φ but the second part of C (t=1 sec and x=.120 m) use a sin equation without the phase constant φ

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For each expression, identify the angular frequency ω , period T , initial phase φ and amplitude y_max of the oscillation. All values are in SI units.

a. y ( t ) = 0.75 cos (14.5 t )

b. v_y ( t ) = −0.75 sin (14.5 t + π /2)

c. a_y ( t ) = 14.5 cos (0.75 t + π /2)

tanweasel847

The figure is an edge-on view of a 14 cm diameter circular loop rotating in a uniform 3.8×10^-2 T magnetic field. I solved part a by using

φ= B A cos θ = Bπr² cosθ = (3.8 x 10^-2) π (.07)2cos (0 degrees)= 5.8 x 10^-4 Wb and got correct answer,

but having trouble finding the right answer for part B. I used the same equation for part B and used cos (30)= got the wrong answer. Is there another equation for finding the answer with the other angles?

Part A What is the magnetic flux through the loop when is 0 degrees?

Express your answer to two significant figures and include the appropriate units.
=5.8×10⁻⁴ Wb
Correct

Part B What is the magnetic flux through the loop when is 30 degrees?
Express your answer to two significant figures and include the appropriate units.
=

Part C
What is the magnetic flux through the loop when is 60 degrees?
Express your answer to two significant figures and include the appropriate units.
=

Part D What is the magnetic flux through the loop when is 90 degrees?
Express your answer to two significant figures and include the appropriate units

graysardine234

A 3 kg mass connected to a spring with force constant 6 N/m isstretched 0.2 m from equilibrium and given speed 1.2 m/s in thepositive x direction.
a) what is the amplitude and the initial phase angle ?

i am confused is it the same as 0.2 b/c x= xmax = A = 0.2 when t= 0and Ï = 0
or i used equation of A = â(x₀² + (v₀ / Ï )² = 0.87

phase angle = arc tan ( -v₀ / Ïx₀ ) THATS HOW I DREW THE PROBLEM PLZ. I NEEDEXPLANANTION

MAIN EQU. X = A COS ( Ït + Ï )

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How does the first equation (for t=0 and x=0) have a cos and φ but the second part of C (t=1 sec and x=.120 m) use a sin equation without the phase constant φ

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Physics: Principles with Applications

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