Question

1. A particle oscillates with the equation: x= 3sin 4t

a. what is the value of its amplitude b. What is the frequency of motion c. What is the angular frequency d. What is the displacement after time t= 3s e. What is the displacement at time t=0 f.Sound waves of speed 35cm are made to travel down a pipe closed at one end and opened at the other and of length 70cm. Calculate The first harmonic and second harmonic

Answer 1

General equation a particle executing oscillation is given by : x = Asinwt ......(1)

here, x is the displacement from mean position, A is the maximum displacement or amplitude of particle ,w is the angular velocity of particle and t is the time

for given particle x = 3sin4t .....(2)

(a). clearly x has maximum value if sin4t is equal to 1

putting sin4t =1 in given equation x = 3sin4t   we get ,

x = 3 hence amplitude of particle = 3 cm

let f be the frequency of given particle

(b). comparing equation (1) with equation (2) we get

angular velocity of given particle =4 .....(3)

2 X pi X f =4

so, f =0.636 Hz

(c). since angular displacement is also known as angular frequency ,therefore from equation (3) we get

angular frequency = 4 rad / second

(d). putting value of t equal to 3 in equation (2) we get

x=3 sin(4 X 3) = 0.6237 cm

so displacement at t=3 s = 0.6237 cm

(e).   putting value of t equal to 0  in equation (2) we get

x=3 sin(4 X 0) = 0.00 cm

so displacement at t=0 s = 0.00 cm