given
m = 3.45 kg
K = 72 N/m
at t = 3s, x = 0.16 m, v = 4.05 m/s
a) let A is the amplitude of motion.
Apply conservation of energy
(1/2)*k*A^2 = (1/2)*k*x^2 + (1/2)*m*v^2
A^2 = x^2 + (m/k)*v^2
A = sqrt(x^2 + (m/k)*v^2)
= sqrt(0.16^2 + (3.45/72)*4.05^2)
= 0.901 m
b) angular frequency, w = sqrt(k/m)
= sqrt(72/3.45)
= 4.57 rad/s
let phi is the initial phase,
at t = 3s,
x = A*sin(w*t + phi)
0.16 = 0.901*sin(4.57*3 + phi)
0.16/0.901 = sin(4.57*3 + phi)
0.178 = sin(4.57*3 + phi)
sin^-1(0.178) = 4.57*3 + phi
0.1789 = 4.57*3 + phi
==> phi = 0.1789 - 4.57*3
= -13.5311 rad
at t = 0 s,
x = A*sin(w*t + phi)
= 0.901*sin(4.57*0 - 13.5311)
= -0.740 m <<<<<<<<<<<-------------Answer
c) at t = 0s,
v = A*w*cos(w*t + phi)
= 0.901*4.57*cos(4.57*0 - 13.5311)
= 2.34 m/s <<<<<<<<<<<-------------Answer
A mass-spring oscillator consists of a 3.45-kg block attached to a spring of spring constant 72.0...
A simple harmonic oscillator consists of a block of mass 4.30 kg attached to a spring of spring constant 440 N/m. When t = 1.90 s, the position and velocity of the block are x = 0.179 m and v = 4.100 m/s. What is the amplitude of the oscillations? What were the position and velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 1.91 kg attached to a spring of spring constant 100 N/m. When t = 1.00 s, the position and velocity of the block are x = 0.124 m and v = 3.417 m/s. A. What is the amplitude of the oscillations? Answer: 0.488 m B. What was the position of the block at t = 0 s? C. What was the velocity of the block at t = 0...
A simple harmonic oscillator consists of a block of mass 3.50 kg attached to a spring of spring constant 400 N/m. When t = 1.70 s, the position and velocity of the block are x = 0.121 m and v = 4.020 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 2.50 kg attached to a spring of spring constant 190 N/m. When t = 1.70 s, the position and velocity of the block are x = 0.184 m and v = 3.140 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 4.60 kg attached to a spring of spring constant 290 N/m. When t = 0.530 s, the position and velocity of the block are x = 0.158 m and v = 3.560 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 3.50 kg attached to a spring of spring constant 440 N/m. When t = 2.20 s, the position and velocity of the block are x = 0.136 m and v = 3.210 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 1.60 kg attached to a spring of spring constant 170 N/m. When t = 1.50 s, the position and velocity of the block are x = 0.126 m and v = 3.090 m/s. (a) What is the amplitude of the oscillations? What were the (b) position and (c) velocity of the block at t = 0 s?
A simple harmonic oscillator consists of a block of mass 2.00 kg attached to a spring of spring constant 100 N/m. When t = 1.00 s, the position and velocity of the block are x = 0.129 m and v = 3.415 m/s respectively. a) What is the amplitude of oscillations? b) What were the position and velocity of the mass at time t = 0?
A simple harmonic oscillator consists of a block of mass 3.70 kg attached to a spring of spring constant 500 N/m. When t = 1.20 s, the position and velocity of the block are x = 0.110 m and v = 2.790 m/s. (a) What is the amplitude of the oscillations? What were the (b)position and (c) velocity of the block at t = 0 s? dont round any numbers
A simple harmonic oscillator consists of a block of mass 3.90 kg attached to a spring of spring constant 120 N/m. When t = 1.00 s, the position and velocity of the block are x = +0.129 m and v = +3.415 m/s. (a) What is the amplitude of the oscillations? ----- m (b) What was the position of the mass at t = 0 s? x = ----- m (c) What was the velocity of the mass at t...