A mass of 0.4 kg, hanging from a spring with a spring constant of 80 N/m, is set into an up-and-down simple harmonic motion. What is the velocity of the mass when at its maximum displacement of 0.1 m?

its maximum displacement is also its Amplitude. When an object is in SHM and reaches its A, its velocity is zero.

Total E=1/2KA^2

Kinetic E=1/2mv^2

Kinetic E= Total E

1/2(80)(0.1)^2=1/2(0.40)(v)^2
v=1.4 m/s

Answer is 0 m/s. At maximum displacement there is no velocity

To find the velocity of the mass when it is at its maximum displacement, we can use the equation for the velocity of an object undergoing simple harmonic motion:

v = ω √(A^2 - x^2)

where v is the velocity, ω is the angular frequency, A is the amplitude (maximum displacement), and x is the current displacement.

First, let's find the angular frequency (ω) using the formula:

ω = √(k/m)

where k is the spring constant and m is the mass.

Substituting the given values:
k = 80 N/m
m = 0.4 kg

ω = √(80 N/m / 0.4 kg)
= √(200 rad/s^2)
≈ 14.14 rad/s

Next, we need to find the displacement (x) when the mass is at its maximum displacement, which is given as 0.1 m.

Now, we can substitute the values into the velocity equation:

v = (14.14 rad/s) √(0.1 m)^2 - x^2)

Since the mass is at maximum displacement (A = 0.1 m), we can rewrite the equation as:

v = (14.14 rad/s) √(0.1 m)^2 - (0.1 m)^2)

v = (14.14 rad/s) √(0.01 m^2 - 0.01 m^2)
v = (14.14 rad/s) √(0)
v = 0 m/s

Therefore, the velocity of the mass when it is at its maximum displacement of 0.1 m is 0 m/s.

1.4 m/s