Frictionless horizontal surface. The toy is pulled, stretching the spring a dist

Question

Frictionless horizontal surface. The toy is pulled, stretching the spring a distance 6.0cm from equilibrium, and released from rest. Find the angular frequency and the period of the oscillation. What is the maximum speed reach by the block? A cork at the end of a spring oscillates with an angular frequency (0= 5.0 rad/s. At 0, the cork is at position jc=2.0cm and is moving with speed 20cm/s in the negative x-direction. The position can be described through the equation x=A cos (cot+cp). Find the amplitude A and the phase angle. A mass at the end of a spring is undergoing simple harmonic oscillations with amplitude A. What fraction of the total mechanical energy is kinetic if the displacement is lA the amplitude?

Explanation / Answer

2)
= 5.0 rad/s
At t = 0, x = 2.0 cm v = 20 cm/s
Position is given by,
x = A * cos(*t + )
Substituing t = 0,
2.0 = A * cos() -------1

Velocity is given by,
dx/dt = - A* * sin(*t + )
Substituing t = 0,
- 20 = - A* * sin() ---------2

tan() = 20/ (2.0 * )
tan() = 2
= 63.4o

2.0 = A * cos(63.4)
A = 4.47 cm

Amplitude, A = 4.47 cm
Angle, = 63.4o

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