A small block is attached to an ideal spring and is moving in SHM on a horizontal, frictionless surface. The amplitude of the motion is 0.200 m and the period is 3.35 s . a.) What is the acceleration when x = 0.160? b.) What is the speed of the block when x= 0.160 m ?

a = 0.563 m/s²

v = 0.225 m/s

Explanation:

The angular frequency is:

ω = 2π / T

ω = 2π / (3.35 s)

ω = 1.88 rad/s

For a spring mass system:

ω = √(k / m)

ω² = k / m

(a) Sum of forces on the mass:

∑F = ma

kx = ma

a = kx / m

a = xω²

When x = 0.160 m:

a = (0.160 m) (1.88 rad/s)²

a = 0.563 m/s²

(b) Energy is conserved.  Initial elastic energy = final elastic energy + kinetic energy.

EE₀ = EE + KE

½ kA² = ½ kx² + ½ mv²

½ (k/m)A² = ½ (k/m)x² + ½ v²

½ ω²A² = ½ ω²x² + ½ v²

ω²A² = ω²x² + v²

v² = ω² (A² − x²)

v = ω √(A² − x²)

v = (1.88 rad/s) √((0.200 m)² − (0.160 m)²)

v = 0.225 m/s

measuring things 1 litre of water

energy can be converted from one form to another, but it cannot be created or destroyed in ordinary chemical or physical means. do not understand what you are asking but hope this