5. The figure 1 below shows three graphs (1,2,3). If a SHM motion is represented

Question

5. The figure 1 below shows three graphs (1,2,3). If a SHM motion is represented by the solution r(t) = Cos(0.8t) , find out which one is the displacement vs time , velocity vs time , acceleration vs time graphs ? (a) displacement vs time +2, velocity vs time +1 , acceleration vs time +3 (b) displacement vs time +3 , velocity vs time +2 , acceleration vs time +1 (c) displacement vs time +1, velocity vs time +2, acceleration vs time +3 (d) none of the options are correct time (5.66% Figure 1 6. match them : for a SHM (1) velocity maximum (2) velocity zero (3) acceleration maximum (4) acceleration zero (x) when displacement from equilibrium maximum i.e displacement = amplitude (xx) when at equilibrium position i.e displacement = 0 (a) 1+x , 2+xx , 3+x , 4+xx (b) 1+x x, 2x , 3x , 4+xx (c) 1+xx , 2+X, 3+xx , 4+x (d) none of the options are correct 7. If you take a pendulum to the planet Jupiter (9 jupiter = 2.5gearth) (same length and mass as in earth), its frequency will increase or decrease when compared to earth's frequency? (assume small angle oscillation) (a) Increase (b) decrease

Explanation / Answer

x(t) = cos(0.8t)

at time t = 0

x(t) = 1

amplitude A = 1 m

velocity v = dx/dt

v = -0.8*sin(0.8t)

at time t = 0

v = 0

acceleration a = dv/dt = -0.8^2*cos(0.8t)

at time t = 0

a = -0.64 m/s^2

therefore

displacement vs time ____> 1

velocity vs time __________>2

acceleration vs time _________> 3

=======================

x = A*cos(0.8t)

v = dx/dt = -0.8*sin0.8t

v = -0.8*sqrt(1-(cos0.8t)^2)

v = -0.8*sqrt(1-x(t)^2/A^2)

v is maximum for x = 0   ( at equilibrium position )

velocity is zero at x = xmax

acceleration a = -0.8*x(t)

a is maximum for x(t) is maximum

a is minimum for x(t) is minimum ( displacement = 0

1 ___> (xx)

2______>(x)

3_______> (x)

4______> (xx)

option ( b )

===================

7)

time period of simple pendulum f = (1/(2*pi))*sqrt(g/L)

on jupiter gjupiter > gearth

frequency increases

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