Block oscillating on an inclined plane A block of weight W = 17.5 N , which can
ID: 1479245 • Letter: B
Question
Block oscillating on an inclined plane
A block of weight W = 17.5 N, which can slide without friction on a 35° incline, is connected to the top of the incline by a massless spring of unstretched length xo = 0.59 m and spring constant k = 450N/m.
a) By how much will the spring be stretched when the system is in equilibrium? Answer = 0.0223 m
b) If the block is pulled slightly down the incline from its equilibrium position and released, what is the frequency of the ensuing oscillations? Answer = ?
I only need the answer to part B with the steps on how to answer it
Explanation / Answer
here ,
B) spring constant , k = 450 N/m
Weight , W = 17.5 N/m
NOw , when the mass is pulled slightly
the acceleration is a
m * a = net force
(W/g) * a = k * (x + xo) - mg * cos(theta)
(W/g) * a = kx + k * x0 - mg * cos(theta)
(W/g ) * a = k * x
where x0 is the initial compression in equilibrium
a = k * g/W * x
for simple harmonic motion
a = w^2 * x
comparing , w = k * g/W
w = 450 * 9.8/17.5
w = 252 rad/s
frequency = w/2pi
frequency = 252/(2pi) Hz
frequency = 40.11 Hz
the frequency of the ensuing oscillations is 40.11 Hz