A simple harmonic oscillator has an amplitude of 3.S0 cm and a maximum speed of

Question

A simple harmonic oscillator has an amplitude of 3.S0 cm and a maximum speed of 26.0 cm/s. What is its speed when the displacement is 1.75 cm? 12.0 cm/s 22.5 cm/s 14.2 cm/s 15.0 cm/s 17.0 cm/s An object that weighs 2.450 N is attached to an ideal massless spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the spring constant of the spring? 2.45 N/m 12.1 N/m 24.1 N/m 0.102 N/m 0.610 N/m A pendulum oscillates with a frequency of 1.0 Hz. If the length of the pendulum is quadrupled. what is the new frequency? 0.25 Hz (LSQJiz 1.0 Hz 4.0 Hz A light bulb emits spherical waves of light. At 1.0 m away from the light bulb the intensity is 2.0 W/m^2. At what distance from the bulb is the intensity equal to 0 50 W/m2? 4.0 m 2.0 m 1.4 nm 0.5 m

Explanation / Answer

(1)
The total energy of the system = 1/2*k*A^2 or 1/2*m*vmax^2

When x = 1/2A then the potential energy =1/2*k*(A/2)^2 = 1/4 of Emax

So the kinetic energy at this time = 3/4 of K max

1/2*m*(v)^2 = 3/4*1/2*m*vmax^2
v = vmax*sqrt(3/4)
v = 26.0cm/s*sqrt(0.75)
v = 22.52cm/s

(2)
W = 2.450 N
T = 0.640 s

We know,
T = 2** sqrt(m/k)
0.640 = 2**sqrt(2.450/k*9.8)
k = 24.1 N/m

(3)
f = 1.0 Hz
f = 1/2**sqrt(L/g)

Lnew = 4*L
fnew = 1/(2**sqrt(4L/g))
fnew = 1/2 * 1/2**sqrt(L/g)
fnew = 1/2 * 1
fnew = 0.5 Hz

(4)
2.0 = k/1.0^2

Let the distance be d
0.5 = k/d^2
0.5 = (2*1.0^2)/d^2
d = 2.0 m

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