Question

An oscillating block-spring system has a mechanical energy of 0.569 J, an amplitude of 10.3 cm, and a maximum speed of 4.63 m/s. Find (a) the spring constant, (b) the mass (in kg) of the block and (c) the frequency (in Hz) of oscillation.

Answer 1

Answer:

(a) the spring constant = 107.3N/m

(b) the mass (in kg) of the block = 0.0531kg

(c) the frequency (in Hz) of oscillation =

7.15Hz

Explanation:

An oscillating block-spring system has a mechanical energy of 0.569 J, an amplitude of 10.3 cm, and a maximum speed of 4.63 m/s.

(a) the spring constant

The formula for finding the spring constant k

k = 2E / x²

Where E  = mechanical energy = 0.569J

x = amplitude = 10.3cm

We convert 10.3cm to meter(m)

100cm = 1m

10.3cm = ?

= 10.3cm ÷ 100cm

= 0.103m

Spring constant (k) = (2 × 0.569j) ÷ (0.103)²

Spring constant (k) = 107.3N/m

(b) the mass (in kg) of the block

Using the  Kinectic Energy = 1/2m(V²max)

Therefore, the formula for Mass(m) = 2E/(V²max)

V = Maximum speed = 4.63 m/s

Mass(m) = (2× 0.569J) ÷ (4.63)²

Mass(m) = 0.0531kg

(c) the frequency (in Hz) of oscillation

The formula of Frequency of oscillation = F = (1/2π) × √k/m

Where k = spring constant = 107.3N/m

m = mass of the block = 0.0531kg

F = (1 ÷ 2π) × √ ( 107.3N/m ÷ 0.0531kg)

F = 7.15Hz