PROGRAM KECEMERLANGAN PELAJARUNIT FIZIK

SEM 1 2015/2016

CHAPTER 9 : SIMPLE HARMONIC MOTIONCHAPTER 10: MECHANICAL WAVE

Prepared by: SII/sem1/2015/16

QUESTION 1 (a)

(i) ω = 2πf so, f = ω/2π = 6π/2π = 3Hz

(ii) v = dx/dt= 0.025 cos 6πt (6π)= 0.15π cos 6πt , t = 4s

so, v = 0.15π cos 6π (4) = 0.47 ms-1

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QUESTION 1 (b) (i)

• m = 300g = 0.3 kg A = 4.0cm = 0.04m k = 10Nm-1

KE at x = 3cm = 0.03m :KE = 1/2 k(A2-x2) = 1/2 (10) (0.042 - 0.032) = 3.5 x 10-3 J

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QUESTION 1 (b) (ii)

• a = - ω2A = - (k/m) A = - (10/0.3) (0.04) = -1.33 ms-2

( a +ve is accepted)

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QUESTION 2 (a)

(i) l = 150 cm = 1.5 m T = 2π √(l/g) = 2π √(1.5/9.81) = 2.46 s

(ii) unchanged - because from the equation of T = 2π √(l/g) , period of oscillation is not affected by mass.

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QUESTION 2 (b) (i)

• v = dx/dt = Aω cos ωt = (14) (2π/4) cos (2π/4)t = 7π cos (π/2)tv/cms-1

t/s

7π

-7π

4

1mark - shape1 mark - axis & label

1 mark - label 7π

QUESTION 2 (b) (ii)

• amax = dv/dt = - Aω2 sin ωt = - (14) (2π/4)2 sin (2π/4)t = - 3.5π2 sin (2π/4)t

a/cms-2

t/s

3.5π2

4

-3.5π2

1mark - shape1 mark - axis & label1 mark - label 3.5π2

QUESTION 3 (a)

(i) Mechanical waves are produced by a source of disturbance and the energy transmitted away from the source.

(ii) Energy

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QUESTION 3 (a) (iii)

• Longitudinal Wave Direction of vibration of the particles is

parallel to the direction of the wave propagation.

• Transverse Wave A wave whose direction of vibration of

particles is perpendicular to the direction of the wave propagation.

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QUESTION 3 (b)

(i) to the right

(ii) v=fλ , f= ω/2π = 600/2π = 95.49 Hz λ=2π/k = 2π/5 = 1.26 m

So, v = 95.49 x 1.26 = 120.32 ms-1

(iii) vy = dy/dt = (0.48)(600)cos(600t-5x) = 288 cos (600t-5x)

So, maximum particle vibrational velocity =288 ms-1

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QUESTION 3 (c)

(i) Stationary wave / Standing wave

(ii) Y = y1 + y2

= 2A cos kx sin ωt = 2(20) cos (2x) sin (15t)= 40 cos 2x sin 15t

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- THE END -